Question 1

Determine whether the lines are parallel,perpendicular,or neither. ?
L1: y = $\frac { 9 } { 2 }$ x - 9
L2: y = - $\frac { 2 } { 9 }$ x - 2
?

Accepted Answer

The slopes of L1 and L2 are $\frac{9}{2}$ and $-\frac{2}{9}$, respectively. Since the product of their slopes is -1 ($\frac{9}{2} * -\frac{2}{9} = -1$), the lines are perpendicular.

Question 2

Find the slope-intercept form of the equation of the line passing through the points.Select the correct answer for the line.? $$\mathrm { P } ( 6,4 ) , \mathrm { Q } ( - 6 , - 6 )$$ ?

Accepted Answer

The answer of Find the slope-intercept form of the equation...

Question 3

Use the intercept form to find the equation of the line with the given intercepts.The intercept form of the equation of a line with intercepts (a,0)and (0,b)is? $\frac { x } { a } + \frac { y } { b } = 1 , a \neq 0 , b \neq 0$ ? ?
X-intercept: ( $- \frac { 5 } { 8 }$ ,0)
Y-intercept: $( 0 , - 3 )$ ?
?

Accepted Answer

The answer of Use the intercept form to find the...

Question 4

The graph shows the sales (in billions of dollars)for Apple Inc.for the years 2001 through 2007.​  Find the slope of the line segment connecting the points for the years 2003 and 2004.Round the answer to two decimal places. ​

Accepted Answer

The answer of The graph shows the sales (in billions...

Question 5

The following is the slope of line representing annual sale y in term of time x in year.Use the slope to interpret any change in annual sales for a one-year increase in time. ​
The line has a slope of m = 134.
​

Accepted Answer

The slope of the line represents the rate of change of y (annual sales) with respect to x (time). A positive slope indicates that as time increases, so does the annual sales. In this case, the slope is 134, which means that for every one-year increase in time, there is an increase in annual sales of 134 units. Therefore, the best choice is C, indicating that sales are increasing by 134 units per year.

Question 6

Use the intercept form to find the equation of the line with the given intercepts.The intercept form of the equation of a line with intercepts (a,0)and (0,b)is ?? $\frac { x } { a } + \frac { y } { b } = 1 , a \neq 0 , b \neq 0$ ?
X-intercept: (-3,0)
Y-intercept: (0,8)
?
?

Accepted Answer

The answer of Use the intercept form to find the...

Question 7

Estimate the slope of the line.​  ​

Accepted Answer

The answer of Estimate the slope of the line.​ ...

Question 8

You are driving on a road that has a 5% uphill grade.This means that the slope of the road is $$\frac { 5 } { 100 }$$ .Approximate the amount of vertical change in your position if you drive 400 feet. ?

Accepted Answer

The vertical change can be calculated by multiplying the slope (5/100) by the distance driven (400 feet), which gives 20 feet.

Question 9

A sub shop purchases a used pizza oven for $885.After 5 years,the oven will have to be replaced.Select the linear equation giving the value V of the equipment during the 5 years it will be in use. ?

Accepted Answer

The value of the oven decreases linearly over 5 years from its purchase price of $885. Since it will be worth $0 after 5 years, it depreciates at a rate of $885 / 5 = $177 per year. Thus, the correct equation is $V = -177t + 885$, where $t$ is the time in years.

Question 10

Use the intercept form to find the equation of the line with the given intercepts.The intercept form of the equation of a line with intercepts (a,0)and (0,b)is ?? $\frac { x } { a } + \frac { y } { b } = 1 , a \neq 0 , b \neq 0$ ?
X-intercept: $\left( - \frac { 1 } { 6 } , 0 \right)$ y-intercept: $\left( 0 , - \frac { 2 } { 7 } \right)$ ?
?

Accepted Answer

The answer of Use the intercept form to find the...

Question 11

Determine whether the lines are parallel,perpendicular,or neither. ?
L1: y = $\frac { 1 } { 2 }$ x - 4
L2: y = - $\frac { 1 } { 2 }$ x - 2
?

Accepted Answer

The slopes of the lines are $\frac{1}{2}$ and $-\frac{1}{2}$. For lines to be parallel, their slopes must be equal. For lines to be perpendicular, the product of their slopes must be -1. Here, the product is $-\frac{1}{4}$, so the lines are neither parallel nor perpendicular.

Question 12

Use the intercept form to find the equation of the line with the given intercepts.The intercept form of the equation of a line with intercepts (a,0)and (0,b)is $\frac { x } { a } + \frac { y } { b } = 1 , a \neq 0 , b \neq 0$ ?? Point on line: (4,6)
X-intercept: (c,0)
Y-intercept: (0,c),c ? 0
?
?

Accepted Answer

Given the intercept form $\frac{x}{a} + \frac{y}{b} = 1$ and the intercepts (c,0) for x and (0,c) for y, substituting these into the intercept form equation gives $\frac{x}{c} + \frac{y}{c} = 1$, which simplifies to $x + y = c$. Since the point (4,6) lies on the line, substituting x=4 and y=6 gives $4 + 6 = c$, so $c = 10$. Therefore, the equation of the line is $x + y - 10 = 0$.

Question 13

The following is the slope of line representing annual sale y in term of time x in year.Use the slope to interpret any change in annual sales for a one-year increase in time. ​
The line has a slope of m = -20.
​

Accepted Answer

The slope of the line is negative (-20), which means that for every one-year increase in time, the annual sales will decrease by 20 units. Therefore, the correct choice is option B, which states that sales are decreasing by 20 units per year.

Question 14

Find the slope-intercept form of the equation of the line that passes through the given point and has the indicated slope m.Select correct answer for the line. ?
P(4, $$\frac { 8 } { 7 }$$ ),m = 0
?

Accepted Answer

The answer of Find the slope-intercept form of the equation...

Question 15

Use the intercept form to find the equation of the line with the given intercepts.The intercept form of the equation of a line with intercepts (a,0)and (0,b)is? $\frac { x } { a } + \frac { y } { b } = 1 , a \neq 0 , b \neq 0$ . ?
X-intercept: (3,0)
Y-intercept: (0,9)
?

Accepted Answer

The answer of Use the intercept form to find the...

Question 16

Find the slope-intercept form of the equation of the line passing through the points.Select the correct answer for the line.? $$P ( 6 , - 2 ) , Q ( - 6,6 )$$ ?

Accepted Answer

The answer of Find the slope-intercept form of the equation...

Question 17

The graph shows the average salaries for senior high school principals from 1996 through 2008.​  ​ Find the slope of the line segment connecting the points for the years 1998 and 2002.
​

Accepted Answer

The answer of The graph shows the average salaries for...

Question 18

Find the slope-intercept form of the equation of the line that passes through the given point and has the indicated slope m.Select correct answer for the line. ​
P(2)4,-8.7),m = -4
​

Accepted Answer

The slope-intercept form of the equation of a line is y = mx + b, where m is the slope and b is the y-intercept.

We are given that the line passes through the point P(2,-8.7) and has a slope of -4.

Plugging in the values we have: 
y = -4x + b

To find b, we can use the coordinates of point P: 
-8.7 = -4(2) + b 
-8.7 = -8 + b 
b = -0.7

Plugging in b, we get: 
y = -4x - 0.7

This matches with choice D, so the best choice is D.

Question 19

The following is the slope of line representing daily revenue y in term of time x in day.Use the slope to interpret any change in daily revenues for a one-day increase in time. ​
The line has a slope of m = 500.
​

Accepted Answer

Since the slope is positive and equal to 500, it means that for each additional day, the daily revenue increases by 500 units. This indicates a positive relationship between time and revenue, where an increase in time is associated with an increase in revenue. Therefore, the correct choice is A, where revenues are increasing by 500 units/day with each one-day increase in time.

Question 20

Determine whether the lines are parallel,perpendicular,or neither. ?
L1: y = $\frac { 1 } { 3 }$ x - 4
L2: y = $\frac { 1 } { 3 }$ x - 3
?

Accepted Answer

The slopes of both lines are $\frac{1}{3}$, indicating they are parallel since parallel lines have equal slopes.

Quiz 3: Linear Equations in Two Variables

Determine whether the lines are parallel,perpendicular,or neither. ? L1: y = $\frac { 9 } { 2 }$ x - 9 L2: y = - $\frac { 2 } { 9 }$ x - 2 ?

Find the slope-intercept form of the equation of the line passing through the points.Select the correct answer for the line.? $\mathrm { P } ( 6,4 ) , \mathrm { Q } ( - 6 , - 6 )$ ?

The graph shows the sales (in billions of dollars) for Apple Inc.for the years 2001 through 2007. Find the slope of the line segment connecting the points for the years 2003 and 2004.Round the answer to two decimal places.

The following is the slope of line representing annual sale y in term of time x in year.Use the slope to interpret any change in annual sales for a one-year increase in time. The line has a slope of m = 134.

Use the intercept form to find the equation of the line with the given intercepts.The intercept form of the equation of a line with intercepts (a,0) and (0,b) is ?? $\frac { x } { a } + \frac { y } { b } = 1 , a \neq 0 , b \neq 0$ ? X-intercept: (-3,0) Y-intercept: (0,8) ? ?

Estimate the slope of the line.

You are driving on a road that has a 5% uphill grade.This means that the slope of the road is $\frac { 5 } { 100 }$ .Approximate the amount of vertical change in your position if you drive 400 feet. ?

A sub shop purchases a used pizza oven for $885.After 5 years,the oven will have to be replaced.Select the linear equation giving the value V of the equipment during the 5 years it will be in use. ?

Determine whether the lines are parallel,perpendicular,or neither. ? L1: y = $\frac { 1 } { 2 }$ x - 4 L2: y = - $\frac { 1 } { 2 }$ x - 2 ?

Use the intercept form to find the equation of the line with the given intercepts.The intercept form of the equation of a line with intercepts (a,0) and (0,b) is $\frac { x } { a } + \frac { y } { b } = 1 , a \neq 0 , b \neq 0$ ?? Point on line: (4,6) X-intercept: (c,0) Y-intercept: (0,c) ,c ? 0 ? ?

The following is the slope of line representing annual sale y in term of time x in year.Use the slope to interpret any change in annual sales for a one-year increase in time. The line has a slope of m = -20.

Find the slope-intercept form of the equation of the line that passes through the given point and has the indicated slope m.Select correct answer for the line. ? P(4, $\frac { 8 } { 7 }$ ) ,m = 0 ?

Use the intercept form to find the equation of the line with the given intercepts.The intercept form of the equation of a line with intercepts (a,0) and (0,b) is? $\frac { x } { a } + \frac { y } { b } = 1 , a \neq 0 , b \neq 0$ . ? X-intercept: (3,0) Y-intercept: (0,9) ?

Find the slope-intercept form of the equation of the line passing through the points.Select the correct answer for the line.? $P ( 6 , - 2 ) , Q ( - 6,6 )$ ?

The graph shows the average salaries for senior high school principals from 1996 through 2008. Find the slope of the line segment connecting the points for the years 1998 and 2002.

Find the slope-intercept form of the equation of the line that passes through the given point and has the indicated slope m.Select correct answer for the line. P(2) 4,-8.7) ,m = -4

The following is the slope of line representing daily revenue y in term of time x in day.Use the slope to interpret any change in daily revenues for a one-day increase in time. The line has a slope of m = 500.

Determine whether the lines are parallel,perpendicular,or neither. ? L1: y = $\frac { 1 } { 3 }$ x - 4 L2: y = $\frac { 1 } { 3 }$ x - 3 ?

Quiz 3: Linear Equations in Two Variables

Determine whether the lines are parallel,perpendicular,or neither. ? L1: y = 92\frac { 9 } { 2 }29​ x - 9 L2: y = - 29\frac { 2 } { 9 }92​ x - 2 ?

Find the slope-intercept form of the equation of the line passing through the points.Select the correct answer for the line.? P(6,4) ,Q(−6,−6) \mathrm { P } ( 6,4 ) , \mathrm { Q } ( - 6 , - 6 ) P(6,4) ,Q(−6,−6) ?

The graph shows the sales (in billions of dollars) for Apple Inc.for the years 2001 through 2007.​ Find the slope of the line segment connecting the points for the years 2003 and 2004.Round the answer to two decimal places. ​

The following is the slope of line representing annual sale y in term of time x in year.Use the slope to interpret any change in annual sales for a one-year increase in time. ​ The line has a slope of m = 134. ​

Estimate the slope of the line.​ ​

You are driving on a road that has a 5% uphill grade.This means that the slope of the road is 5100\frac { 5 } { 100 }1005​ .Approximate the amount of vertical change in your position if you drive 400 feet. ?

A sub shop purchases a used pizza oven for $885.After 5 years,the oven will have to be replaced.Select the linear equation giving the value V of the equipment during the 5 years it will be in use. ?

Determine whether the lines are parallel,perpendicular,or neither. ? L1: y = 12\frac { 1 } { 2 }21​ x - 4 L2: y = - 12\frac { 1 } { 2 }21​ x - 2 ?

The following is the slope of line representing annual sale y in term of time x in year.Use the slope to interpret any change in annual sales for a one-year increase in time. ​ The line has a slope of m = -20. ​

Find the slope-intercept form of the equation of the line that passes through the given point and has the indicated slope m.Select correct answer for the line. ? P(4, 87\frac { 8 } { 7 }78​ ) ,m = 0 ?

Find the slope-intercept form of the equation of the line passing through the points.Select the correct answer for the line.? P(6,−2) ,Q(−6,6) P ( 6 , - 2 ) , Q ( - 6,6 ) P(6,−2) ,Q(−6,6) ?

The graph shows the average salaries for senior high school principals from 1996 through 2008.​ ​ Find the slope of the line segment connecting the points for the years 1998 and 2002. ​

Find the slope-intercept form of the equation of the line that passes through the given point and has the indicated slope m.Select correct answer for the line. ​ P(2) 4,-8.7) ,m = -4 ​

The following is the slope of line representing daily revenue y in term of time x in day.Use the slope to interpret any change in daily revenues for a one-day increase in time. ​ The line has a slope of m = 500. ​

Determine whether the lines are parallel,perpendicular,or neither. ? L1: y = 13\frac { 1 } { 3 }31​ x - 4 L2: y = 13\frac { 1 } { 3 }31​ x - 3 ?

Determine whether the lines are parallel,perpendicular,or neither. ? L1: y = $\frac { 9 } { 2 }$ x - 9 L2: y = - $\frac { 2 } { 9 }$ x - 2 ?

Find the slope-intercept form of the equation of the line passing through the points.Select the correct answer for the line.? $\mathrm { P } ( 6,4 ) , \mathrm { Q } ( - 6 , - 6 )$ ?

The graph shows the sales (in billions of dollars) for Apple Inc.for the years 2001 through 2007. Find the slope of the line segment connecting the points for the years 2003 and 2004.Round the answer to two decimal places.

The following is the slope of line representing annual sale y in term of time x in year.Use the slope to interpret any change in annual sales for a one-year increase in time. The line has a slope of m = 134.

Estimate the slope of the line.

You are driving on a road that has a 5% uphill grade.This means that the slope of the road is $\frac { 5 } { 100 }$ .Approximate the amount of vertical change in your position if you drive 400 feet. ?

Determine whether the lines are parallel,perpendicular,or neither. ? L1: y = $\frac { 1 } { 2 }$ x - 4 L2: y = - $\frac { 1 } { 2 }$ x - 2 ?

The following is the slope of line representing annual sale y in term of time x in year.Use the slope to interpret any change in annual sales for a one-year increase in time. The line has a slope of m = -20.

Find the slope-intercept form of the equation of the line that passes through the given point and has the indicated slope m.Select correct answer for the line. ? P(4, $\frac { 8 } { 7 }$ ) ,m = 0 ?

Find the slope-intercept form of the equation of the line passing through the points.Select the correct answer for the line.? $P ( 6 , - 2 ) , Q ( - 6,6 )$ ?

The graph shows the average salaries for senior high school principals from 1996 through 2008. Find the slope of the line segment connecting the points for the years 1998 and 2002.

Find the slope-intercept form of the equation of the line that passes through the given point and has the indicated slope m.Select correct answer for the line. P(2) 4,-8.7) ,m = -4

The following is the slope of line representing daily revenue y in term of time x in day.Use the slope to interpret any change in daily revenues for a one-day increase in time. The line has a slope of m = 500.

Determine whether the lines are parallel,perpendicular,or neither. ? L1: y = $\frac { 1 } { 3 }$ x - 4 L2: y = $\frac { 1 } { 3 }$ x - 3 ?