Question 1

Use the point-slope form to write an equation of the line with the slope $-$ 6 and that passes through the point ( $-$ 9, 2). Then write your result in slope-intercept form.
A) $y = - 6 x - 51$
B) $y = - 6 x - 50$
C) $y = - 6 x - 52$
D) $y = 6 x - 51$
E) $y = 6 x - 52$

Accepted Answer

The answer of Use the point-slope form to write an...

Question 2

Find the slope and the y -intercept of the line of the equation. y = -0.00017 x $-$ 0.0017

Accepted Answer

The answer of Find the slope and the y -intercept...

Question 3

Find the equation of the line that contains the two given points. Express the equation in the form $A x + B y = C$ , where A , B , and C are integers. $( 4,8 ) , ( 5,11 )$

Accepted Answer

The answer of Find the equation of the line that...

Question 4

Find the equation of the line that contains the two given points. $( 3,1 ) , ( 10,4 )$
A)7 y + 3 x = -2
B)3 x - 7 y = -2
C)7 y - 3 x = -2
D)7 y - 3 x = 16
E)7 y + 3 x = 16

Accepted Answer

We can use the point-slope form of a line to find the equation:
$$y - y_1 = \frac{y_2 - y_1}{x_2 - x_1}(x - x_1)$$
Plugging in the given points, we get:
$$y - 1 = \frac{4-1}{10-3}(x-3)$$
Simplifying this equation gives:
$$y - 1 = \frac{1}{7}(x-3)$$
Multiplying both sides by 7 and rearranging gives:
$$7y - 3x = -2$$
which matches choice C.

Question 5

If the rise of the roof shown in the illustration is 5 feet, and the run is 9 feet, find the pitch of the roof. 
A) $- \frac { 5 } { 9 }$
B)45
C) $\frac { 5 } { 9 }$
D)14
E) $\frac { 9 } { 5 }$

Accepted Answer

Pitch is defined as the vertical rise per unit of horizontal run. So, we can calculate the pitch of the roof by dividing the rise by the run.

Pitch = Rise/Run = 5/9

Therefore, the pitch of the roof is 5/9 or Choice C).

Question 6

Use the point-slope form to write an equation of the line with the slope $- \frac { 3 } { 5 }$ and that passes through the point $( - 2 , - 6 )$ .
A) $y - 2 = - \frac { 3 } { 5 } ( x + 6 )$
B) $y + 2 = - \frac { 3 } { 5 } ( x + 6 )$
C) $y - 6 = - \frac { 3 } { 5 } ( x + 2 )$
D) $y + 6 = - \frac { 3 } { 5 } ( x + 2 )$
E) $y + 6 = \frac { 3 } { 5 } ( x + 2 )$

Accepted Answer

The point-slope form of a line is $y - y_1 = m(x - x_1)$. Substituting $m = -\frac{3}{5}$, $x_1 = -2$, and $y_1 = -6$, we get $y + 6 = -\frac{3}{5}(x + 2)$.

Question 7

The equation of the horizontal line passing through (10, -9)is x = -9.

Accepted Answer

The equation of a horizontal line is of the form y = constant. Therefore, the equation of the horizontal line passing through (10, -9) would be y = -9, not x = -9.

Question 8

Use the point-slope form to write an equation of the line with the slope $-$ 8 and that passes through the point ( $-$ 2, 4). Then write your result in slope-intercept form.
A) $y = - 8 x - 14$
B) $y = - 8 x - 10$
C) $y = - 8 x - 12$
D) $y = 8 x - 14$
E) $y = 8 x - 12$

Accepted Answer

Using the point-slope form, we have:

$$y - y_1 = m(x-x_1)$$

where $m$ is the slope and $(x_1,y_1)$ is the given point. Substituting $m=-8$, $x_1=-2$, and $y_1=4$, we get:

$$y - 4 = -8(x-(-2))$$

Simplifying:

$$y-4 = -8x - 16$$

$$y = -8x -12$$

This is already in slope-intercept form ($y=mx+b$) with $m=-8$ and $b=-12$. Therefore, the answer is C.

Question 9

The height (in inches)of a human is almost linearly related to his\her body weight (in pounds). For example, a 5'2'' tall person would weight around 118 lb; and a 5'9'' tall person would weight around 139 lb. Can you predict how tall could be a person whose weight is 181 lb?
A)6'11''
B)11'6''
C)10'6''
D)6'10''

Accepted Answer

The height (in inches) of a human is almost linearly related to his/her body weight (in pounds). For example, a 5'2'' tall person would weight around 118 lb; and a 5'9'' tall person would weight around 139 lb. Can you predict how tall could be a person whose weight is 181 lb?A)6'11''B)11'6''C)10'6''D)6'10''                          IN first line,   provide the choice number of correct choice(s) ONLY, without extra text AND without choice text                           IN the second line, provide a brief explanation for the correct answer(s).                           ,OUTPUT formate example : "A,D  explanation for the answer etc."                             AThe height (in inches) of a human is almost linearly related to his/her body weight (in pounds). For example, a 5'2'' tall person would weight around 118 lb; and a 5'9'' tall person would weight around 139 lb. Can you predict how tall could be a person whose weight is 181 lb?A)6'11''B)11'6''C)10'6''D)6'10''                          IN first line,   provide the choice number of correct choice(s) ONLY, without extra text AND without choice text                           IN the second line, provide a brief explanation for the correct answer(s).                           ,OUTPUT formate example : "A,D  explanation for the answer etc."                             AThe height (in inches) of a human is almost linearly related to his/her body weight (in pounds). For example, a 5'2'' tall person would weight around 118 lb; and a 5'9'' tall person would weight around 139 lb. Can you predict how tall could be a person whose weight is 181 lb?A)6'11''B)11'6''C)10'6''D)6'10''                          IN first line,   provide the choice number of correct choice(s) ONLY, without extra text AND without choice text                           IN the second line, provide a brief explanation for the correct answer(s).                           ,OUTPUT formate example : "A,D  explanation for the answer etc."                             AThe height (in inches) of a human is almost linearly related to his/her body weight (in pounds). For example, a 5'2'' tall person would weight around 118 lb; and a 5'9'' tall person would weight around 139 lb. Can you predict how tall could be a person whose weight is 181 lb?A)6'11''B)11'6''C)10'6''D)6'10''                          IN first line,   provide the choice number of correct choice(s) ONLY, without extra text AND without choice text                           IN the second line, provide a brief explanation for the correct answer(s).                           ,OUTPUT formate example : "A,D  explanation for the answer etc."                             AThe height (in inches) of a human is almost linearly related to his/her body weight (in pounds). For example, a 5'2'' tall person would weight around 118 lb; and a 5'9'' tall person would weight around 139 lb. Can you predict how tall could be a person whose weight is 181 lb?A)6'11''B)11'6''C)10'6''D)6'10''                          IN first line,   provide the choice number of correct choice(s) ONLY, without extra text AND without choice text                           IN the second line, provide a brief explanation for the correct answer(s).                           ,OUTPUT formate example : "A,D  explanation for the answer etc."                             AThe height (in inches) of a human is almost linearly related to his/her body weight (in pounds). For example, a 5'2'' tall person would weight around 118 lb; and a 5'9'' tall person would weight around 139 lb. Can you predict how tall could be a person whose weight is 181 lb?A)6'11''B)11'6''C)10'6''D)6'10''                          IN first line,   provide the choice number of correct choice(s) ONLY, without extra text AND without choice text                           IN the second line, provide a brief explanation for the correct answer(s).                           ,OUTPUT formate example : "A,D  explanation for the answer etc."                             AThe height (in inches) of a human is almost linearly related to his/her body weight (in pounds). For example, a 5'2'' tall person would weight around 118 lb; and a 5'9'' tall person would weight around 139 lb. Can you predict how tall could be a person whose weight is 181 lb?A)6'11''B)11'6''C)10'6''D)6'10''                          IN first line,   provide the choice number of correct choice(s) ONLY, without extra text AND without choice text                           IN the second line, provide a brief explanation for the correct answer(s).                           ,OUTPUT formate example : "A,D  explanation for the answer etc."                             AThe height (in inches) of a human is almost linearly related to his/her body weight (in pounds). For example, a 5'2'' tall person would weight around 118 lb; and a 5'9'' tall person would weight around 139 lb. Can you predict how tall could be a person whose weight is 181 lb?A)6'11''B)11'6''C)10'6''D)6'10''                          IN first line,   provide the choice number of correct choice(s) ONLY, without extra text AND without choice text                           IN the second line, provide a brief explanation for the correct answer(s).                           ,OUTPUT formate example : "A,D  explanation for the answer etc."                             AThe height (in inches) of a human is almost linearly related to his/her body weight (in pounds). For example, a 5'2'' tall person would weight around 118 lb; and a 5'9'' tall person would weight around 139 lb. Can you predict how tall could be a person whose weight is 181 lb?A)6'11''B)11'6''C)10'6''D)6'10''                          IN first line,   provide the choice number of correct choice(s) ONLY, without extra text AND without choice text                           IN the second line, provide a brief explanation for the correct answer(s).                           ,OUTPUT formate example : "A,D  explanation for the answer etc."                             AThe height (in inches) of a human is almost linearly related to his/her body weight (in pounds). For example, a 5'2'' tall person would weight around 118 lb; and a 5'9'' tall person would weight around 139 lb. Can you predict how tall could be a person whose weight is 181 lb?A)6'11''B)11'6''C)10'6''D)6'10''                          IN first line,   provide the choice number of correct choice(s) ONLY, without extra text AND without choice text                           IN the second line, provide a brief explanation for the correct answer(s).                           ,OUTPUT formate example : "A,D  explanation for the answer etc."                             AThe height (in inches) of a human is almost linearly related to his/her body weight (in pounds). For example, a 5'2'' tall person would weight around 118 lb; and a 5'9'' tall person would weight around 139 lb. Can you predict how tall could be a person whose weight is 181 lb?A)6'11''B)11'6''C)10'6''D)6'10''                          IN first line,   provide the choice number of correct choice(s) ONLY, without extra text AND without choice text                           IN the second line, provide a brief explanation for the correct answer(s).                           ,OUTPUT formate example : "A,D  explanation for the answer etc."                             AThe height (in inches) of a human is almost linearly related to his/her body weight (in pounds). For example, a 5'2'' tall person would weight around 118 lb; and a 5'9'' tall person would weight around

Question 10

Find the slope m and the y -intercept of the line y = 2.663 + 8.415 x
A)m = 8.415, y int = 2.663
B)m = 2.663; y int = 8.415
C)m = -8.415, y int = 2.663
D)m = 8.415, y int = 0

Accepted Answer

In the equation y = 2.663 + 8.415x, the coefficient of x (8.415) represents the slope (m) of the line. Thus, m = 8.415. The constant term (2.663) represents the y-intercept, so the y-intercept is 2.663. Therefore, the correct answer is A.

Question 11

The grade of a highway up a hill is 27%. How much change in horizontal distance is there if the vertical height of the hill is 250 feet? Express the answer to the nearest foot.
A)945 ft
B)926 ft
C)826 ft
D)936 ft
E)901 ft

Accepted Answer

The horizontal distance is given by dividing the vertical height by the grade (which is a ratio of vertical rise to horizontal run).

Horizontal distance = vertical height / grade
Horizontal distance = 250 / 0.27
Horizontal distance ≈ 925.9 ft

Rounding to the nearest foot gives us 926 ft.

Question 12

Use the point-slope form to write an equation of the line with the slope 8 and that passes through the point (1, 4).
A)y + 1 = 8( x $-$ 4)
B)y $-$ 4 = 8( x + 1)
C)y + 4 = 8( x $-$ 1)
D)y $-$ 4 = 8( x $-$ 1)
E)y $-$ 1 = 8( x $-$ 4)

Accepted Answer

The point-slope form of a line is y - y1 = m(x - x1), where (x1,y1) is a point on the line and m is the slope of the line.

In this case, we are given that the slope of the line is 8 and it passes through the point (1,4).

Substituting these values into the point-slope formula, we get:

y - 4 = 8(x - 1)

Simplifying and rearranging, we get:

y - 4 = 8x - 8

y = 8x - 4

Therefore, the correct choice is D.

Question 13

Determine whether the graphs of y = 3 x - 7 and y = $ \frac{6}{7} $ x - 2 of are parallel, perpendicular, or neither.
A)parallel
B)neither parallel, nor perpendicular
C)perpedicular

Accepted Answer

Two lines are parallel if their slopes are equal, and perpendicular if their slopes are negative reciprocals of each other. Comparing the two given equations, we see that one slope is 3 and the other is 6/7. These slopes are not equal, nor are they negative reciprocals of each other, so the lines are neither parallel nor perpendicular.

Question 14

The equation of the vertical line that passes through (-9, -10)is x = -9.

Accepted Answer

A vertical line has a constant x-coordinate, so any vertical line passing through the point (-9,-10) must have an x-coordinate of -9. Therefore, its equation is x=-9.

Question 15

If the ratio of rise to run is to be $\frac { 1 } { 3 }$ for some stairs and the measure of the run is 22 centimeters, find the measure of the rise to the nearest centimeter.
A)66 cm
B)6 cm
C)7 cm
D)17 cm
E)22 cm

Accepted Answer

The ratio of rise to run is $\frac{1}{3}$, which means that for every 3 units of run, we have 1 unit of rise. If the run is 22 centimeters, we can set up the proportion:

$\frac{\text{rise}}{22}=\frac{1}{3}$

Cross-multiplying gives us:

3 × rise = 22

rise = $\frac{22}{3}$

Rounding to the nearest centimeter gives us a rise of 7 centimeters. Therefore, the answer is C.

Question 16

Find the equation of the line that contains the two given points. $( - 8,0 ) , ( 0 , - 3 )$
A)8 y + 3 x = -24
B)8 y + 3 x = 24
C)8 y - 3 x = -3
D)8 y - 3 x = -24
E)8 y - 3 x = 24

Accepted Answer

The slope of the line through the points $(-8,0)$ and $(0,-3)$ is $\frac{-3-0}{0-(-8)} = \frac{-3}{8}$. Using point-slope form, $y - y_1 = m(x - x_1)$, with $m = -\frac{3}{8}$ and point $(-8, 0)$, we get $y - 0 = -\frac{3}{8}(x + 8)$. Multiplying both sides by 8 to clear the fraction gives $8y = -3x - 24$, which rearranges to $8y + 3x = -24$.

Question 17

Write an equation of a horizontal line passing through (-2, 4)and an equation of a vertical line passing through (4, -3).Graph both lines.
A) 
B) 
C) 
D)

Accepted Answer

The answer of Write an equation of a horizontal line...

Question 18

An automated production line uses distilled water at a rate of 700 gallons every 4 hours to make toothpaste. After the line had run for 6 hours, planners noted that 1700 gallons of distilled water remained in the storage tank. Find the number of gallons of distilled water in the storage tank when the production line began.
A)9200 gallons
B)4800 gallons
C)2750 gallons
D)6800 gallons
E)none of these

Accepted Answer

The answer of An automated production line uses distilled water...

Question 19

Find the slope of the line of the equation. y = 0.4 x $-$ 2

Accepted Answer

The answer of Find the slope of the line of...

Question 20

You and your friends each eat 2 slices of pizza for dinner, there are 8 slices in a pie, and the delivery fee is $5. You must tip 10% on the pizza order but not on the delivery fee. Express the total cost in an expression.
A)y = 2 x + 5
B)y = 2.2 x + 5
C)y = 0.2 x + 5
D)y = 2 x

Accepted Answer

The cost of the pizza would be 2 slices per person x number of people, or 2x. We must then add the delivery fee of $5, giving us 2x + 5. To find the tip, we would take 10% of the cost of the pizza (2x) only, so the expression becomes 2.2x. Therefore, the total cost expression is y = 2.2x + 5. Choice B is the correct answer.

Quiz 3: Graphs, Linear Equations, and Inequalities in Two Variables; Functions From Campus to Careers: Physical Therapis

Use the point-slope form to write an equation of the line with the slope $-$ 6 and that passes through the point ( $-$ 9, 2) . Then write your result in slope-intercept form.

Find the slope and the y -intercept of the line of the equation. y = -0.00017 x $-$ 0.0017

Find the equation of the line that contains the two given points. Express the equation in the form $A x + B y = C$ , where A , B , and C are integers. $( 4,8 ) , ( 5,11 )$

Find the equation of the line that contains the two given points. $( 3,1 ) , ( 10,4 )$

Use the point-slope form to write an equation of the line with the slope $- \frac { 3 } { 5 }$ and that passes through the point $( - 2 , - 6 )$ .

The equation of the horizontal line passing through (10, -9)is x = -9.

Use the point-slope form to write an equation of the line with the slope $-$ 8 and that passes through the point ( $-$ 2, 4) . Then write your result in slope-intercept form.

The height (in inches) of a human is almost linearly related to his\her body weight (in pounds) . For example, a 5'2'' tall person would weight around 118 lb; and a 5'9'' tall person would weight around 139 lb. Can you predict how tall could be a person whose weight is 181 lb?

Find the slope m and the y -intercept of the line y = 2.663 + 8.415 x

The grade of a highway up a hill is 27%. How much change in horizontal distance is there if the vertical height of the hill is 250 feet? Express the answer to the nearest foot.

Use the point-slope form to write an equation of the line with the slope 8 and that passes through the point (1, 4) .

Determine whether the graphs of y = 3 x - 7 and y = $\frac{6}{7}$ x - 2 of are parallel, perpendicular, or neither.

The equation of the vertical line that passes through (-9, -10)is x = -9.

If the ratio of rise to run is to be $\frac { 1 } { 3 }$ for some stairs and the measure of the run is 22 centimeters, find the measure of the rise to the nearest centimeter.

Find the equation of the line that contains the two given points. $( - 8,0 ) , ( 0 , - 3 )$

Write an equation of a horizontal line passing through (-2, 4) and an equation of a vertical line passing through (4, -3) .Graph both lines.

Find the slope of the line of the equation. y = 0.4 x $-$ 2

You and your friends each eat 2 slices of pizza for dinner, there are 8 slices in a pie, and the delivery fee is $5. You must tip 10% on the pizza order but not on the delivery fee. Express the total cost in an expression.

Quiz 3: Graphs, Linear Equations, and Inequalities in Two Variables; Functions From Campus to Careers: Physical Therapis

Use the point-slope form to write an equation of the line with the slope −-− 6 and that passes through the point ( −-− 9, 2) . Then write your result in slope-intercept form.

Find the slope and the y -intercept of the line of the equation. y = -0.00017 x −-− 0.0017

Find the equation of the line that contains the two given points. Express the equation in the form Ax+By=CA x + B y = CAx+By=C , where A , B , and C are integers. (4,8),(5,11)( 4,8 ) , ( 5,11 )(4,8),(5,11)

Find the equation of the line that contains the two given points. (3,1) ,(10,4) ( 3,1 ) , ( 10,4 ) (3,1) ,(10,4)

If the rise of the roof shown in the illustration is 5 feet, and the run is 9 feet, find the pitch of the roof.

Use the point-slope form to write an equation of the line with the slope −35- \frac { 3 } { 5 }−53​ and that passes through the point (−2,−6) ( - 2 , - 6 ) (−2,−6) .

The equation of the horizontal line passing through (10, -9)is x = -9.

Use the point-slope form to write an equation of the line with the slope −-− 8 and that passes through the point ( −-− 2, 4) . Then write your result in slope-intercept form.

The height (in inches) of a human is almost linearly related to his\her body weight (in pounds) . For example, a 5'2'' tall person would weight around 118 lb; and a 5'9'' tall person would weight around 139 lb. Can you predict how tall could be a person whose weight is 181 lb?

Find the slope m and the y -intercept of the line y = 2.663 + 8.415 x

The grade of a highway up a hill is 27%. How much change in horizontal distance is there if the vertical height of the hill is 250 feet? Express the answer to the nearest foot.

Use the point-slope form to write an equation of the line with the slope 8 and that passes through the point (1, 4) .

Determine whether the graphs of y = 3 x - 7 and y = 67 \frac{6}{7} 76​ x - 2 of are parallel, perpendicular, or neither.

The equation of the vertical line that passes through (-9, -10)is x = -9.

If the ratio of rise to run is to be 13\frac { 1 } { 3 }31​ for some stairs and the measure of the run is 22 centimeters, find the measure of the rise to the nearest centimeter.

Find the equation of the line that contains the two given points. (−8,0) ,(0,−3) ( - 8,0 ) , ( 0 , - 3 ) (−8,0) ,(0,−3)

Write an equation of a horizontal line passing through (-2, 4) and an equation of a vertical line passing through (4, -3) .Graph both lines.

Find the slope of the line of the equation. y = 0.4 x −-− 2

You and your friends each eat 2 slices of pizza for dinner, there are 8 slices in a pie, and the delivery fee is $5. You must tip 10% on the pizza order but not on the delivery fee. Express the total cost in an expression.

Use the point-slope form to write an equation of the line with the slope $-$ 6 and that passes through the point ( $-$ 9, 2) . Then write your result in slope-intercept form.

Find the slope and the y -intercept of the line of the equation. y = -0.00017 x $-$ 0.0017

Find the equation of the line that contains the two given points. Express the equation in the form $A x + B y = C$ , where A , B , and C are integers. $( 4,8 ) , ( 5,11 )$

Find the equation of the line that contains the two given points. $( 3,1 ) , ( 10,4 )$

Use the point-slope form to write an equation of the line with the slope $- \frac { 3 } { 5 }$ and that passes through the point $( - 2 , - 6 )$ .

Use the point-slope form to write an equation of the line with the slope $-$ 8 and that passes through the point ( $-$ 2, 4) . Then write your result in slope-intercept form.

Determine whether the graphs of y = 3 x - 7 and y = $\frac{6}{7}$ x - 2 of are parallel, perpendicular, or neither.

If the ratio of rise to run is to be $\frac { 1 } { 3 }$ for some stairs and the measure of the run is 22 centimeters, find the measure of the rise to the nearest centimeter.

Find the equation of the line that contains the two given points. $( - 8,0 ) , ( 0 , - 3 )$

Find the slope of the line of the equation. y = 0.4 x $-$ 2