Question 1

Write an equation for the line described. Write the equation in the form specified.
-parallel to $2 x + 7 y = 65$, through $( 8,4 )$; slope-intercept form

Accepted Answer

The slope of the line $2x + 7y = 65$ is $-\frac{2}{7}$. A parallel line has the same slope. Using the point-slope form with point $(8,4)$, the equation is $y = -\frac{2}{7}x + \frac{44}{7}$.

Question 2

Write an equation for the line described. Write the equation in the form specified.
-parallel to $x = - 2$, through $( 5,3 )$

Accepted Answer

A line parallel to $x = -2$ is also a vertical line, which means its equation will have the form $x = \text{constant}$. Since it passes through $(5,3)$, the equation is $x = 5$.

Question 3

Write all linear equations in slope-intercept form.
-With 23.5% commitment, a company can clean up 40% of an energy leak. With 28.5% commitment, it can clean up 80% of an energy leak. Find a linear equation that models the percent cleanup for x percent commitment.

Accepted Answer

The slope-intercept form of a linear equation is $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept. To find the slope ($m$), we use the formula $\frac{y_2 - y_1}{x_2 - x_1}$, where $(x_1, y_1)$ and $(x_2, y_2)$ are two points on the line. Here, the points are (23.5, 40) and (28.5, 80), representing percent commitment and percent cleanup, respectively. Calculating the slope: $m = \frac{80 - 40}{28.5 - 23.5} = \frac{40}{5} = 8$.To find the y-intercept ($b$), we can use one of the points and the slope in the equation $y = mx + b$. Using the point (23.5, 40):$40 = 8(23.5) + b$Solving for $b$, we get:$b = 40 - 8(23.5) = 40 - 188 = -148$.Thus, the equation is $y = 8x - 148$.

Question 4

Write all linear equations in slope-intercept form.
-The table lists the average annual cost (in dollars) of room and board at public four-year colleges in the city of Bookhaven for selected years. PUBLIC FOUR-YEAR COLLEGE ROOM AND BOARD

Determine a linear function $\mathrm { f }$ defined by $\mathrm { f } ( \mathrm { x } ) = \mathrm { mx } + \mathrm { b }$ that models the data using $( 1,1350 )$ and $( 6,3105 )$.

Accepted Answer

The answer of Write all linear equations in slope-intercept form.
-The...

Question 5

Write an equation for the line described. Write the equation in the form specified.
-perpendicular to $y = 2$, through $( 3,4 )$

Accepted Answer

The line $y = 2$ is horizontal. A line perpendicular to it would be vertical, which means it has the form $x = a$, where $a$ is the x-coordinate of the point it passes through. Since it passes through $(3,4)$, the equation is $x = 3$.

Question 6

Write all linear equations in slope-intercept form.
-A company can make 9 satellite dishes for $92,300, while 16 satellite dishes cost $97,130. Find a linear equation that models the cost to produce x satellite dishes.

Accepted Answer

To find the slope ($m$) of the line, we use the formula $m = \frac{y_2 - y_1}{x_2 - x_1}$, where $(x_1, y_1)$ and $(x_2, y_2)$ are points on the line. Substituting the given points (9, 92300) and (16, 97130), we get $m = \frac{97130 - 92300}{16 - 9} = \frac{4830}{7} = 690$. To find the y-intercept ($b$), we use one of the points and the slope in the equation $y = mx + b$. Substituting $x = 9$, $y = 92300$, and $m = 690$ gives $92300 = 690(9) + b$, solving for $b$ gives $b = 86090$. Therefore, the equation is $y = 690x + 86090$.

Question 7

Write an equation for the line described. Write the equation in the form specified.
-perpendicular to $x = - 3$, through $( 8,7 )$

Accepted Answer

The answer of Write an equation for the line described....

Question 8

Write an equation for the line described. Write the equation in the form specified.
-perpendicular to $2 x - 5 y = - 19$, through $( 3 , - 5 )$; slope-intercept form

Accepted Answer

The answer of Write an equation for the line described....

Question 9

Write all linear equations in slope-intercept form.
-Suppose that a sales person observes that if an item is priced at $10 per item then 4 items are sold. If 2 items are sold for $12 per item then find a linear equation to model the number y of items sold for x dollars per item. Find
The slope-intercept form of the equation of the line.

Accepted Answer

The slope $m$ of the line can be found using the two given points $(10, 4)$ and $(12, 2)$ as $m = \frac{2 - 4}{12 - 10} = \frac{-2}{2} = -1$. Using the point-slope form $y - y_1 = m(x - x_1)$ with one of the points, for example, $(10, 4)$, we get $y - 4 = -1(x - 10)$, which simplifies to $y = -x + 14$.

Question 10

Write all linear equations in slope-intercept form.
-A driver wants to gauge the fuel efficiency of her vehicle at speeds of 30 mph and above. She notices that traveling at an average speed of 45 mph results in a rating of 39 mpg, whereas at an average speed of 50 mph,
Her car rates 29 mpg. Find a linear equation to model the gas mileage y for an average speed of x mph. Find the
Slope-intercept form of the equation of the line.

Accepted Answer

The answer of Write all linear equations in slope-intercept form.
-A...

Question 11

Write an equation for the line described. Write the equation in the form specified.
-parallel to $\mathrm { y } = - 9$, through $( 5,3 )$

Accepted Answer

A line parallel to $y = -9$ would have the same form, which means it does not change in x (it's horizontal). Since it passes through (5,3), the y-value for the entire line must be 3, hence $y = 3$.

Question 12

Write all linear equations in slope-intercept form.
-A house was purchased for $83,000. After 6 years the value of the house was $101,000. Find a linear equation that models the value of the house after x years.

Accepted Answer

The slope (rate of change in value) is calculated as $\frac{101,000 - 83,000}{6} = 3,000$. The y-intercept (initial value) is the purchase price, $83,000. Thus, the equation is $y = 3000x + 83,000$.

Question 13

Write an equation for the line described. Write the equation in the form specified.
-parallel to $y + 8 x = 4$, through $( 4,5 )$; slope-intercept form

Accepted Answer

The answer of Write an equation for the line described....

Question 14

The graph of a linear function f is shown. Write the equation that defines f. Write the equation in slope-intercept form.
-

Accepted Answer

The answer of The graph of a linear function f...

Question 15

Write an equation for the line described. Write the equation in the form specified.
-perpendicular to $8 x - 7 y = 127$, through $( 8,9 )$; standard form

Accepted Answer

The slope of the line $8x - 7y = 127$ is $\frac{8}{7}$. A line perpendicular to it will have a slope of $-\frac{7}{8}$. Using the point-slope form with point $(8,9)$, the equation is $y - 9 = -\frac{7}{8}(x - 8)$. Converting to standard form gives $7x + 8y = 128$.

Question 16

Write an equation for the line described. Write the equation in the form specified.
-perpendicular to $- 2 x + y = 8$, through $( 5,4 )$; slope-intercept form

Accepted Answer

The answer of Write an equation for the line described....

Question 17

Write all linear equations in slope-intercept form.
-In a lab experiment 3 grams of acid were produced in 17 minutes and 18 grams in 45 minutes. Find a linear equation that models the number of grams produced in x minutes.

Accepted Answer

The answer of Write all linear equations in slope-intercept form.
-In...

Question 18

Write all linear equations in slope-intercept form.
-The amount of time t it takes a flame to go out in a closed container is a linear function of the volume of the container x. A flame in 798 mL container takes 14 seconds to go out and a flame in a 1344 mL container takes
27 seconds. Write a linear function that relates t to x.

Accepted Answer

The slope of the line is calculated as the change in time divided by the change in volume: (27-14)/(1344-798) = 1/42. Using the point-slope form and substituting one of the points, the equation becomes $t = \frac{1}{42}x - 5$.

Question 19

Write an equation for the line described. Write the equation in the form specified.
-parallel to $3 x + 8 y = 57$; through $( 3,7 )$; standard form

Accepted Answer

Lines that are parallel have the same slope, meaning the coefficients of $x$ and $y$ in the equation must remain the same. The equation $3x + 8y = 57$ can be used as a basis. To find the equation of the line that passes through $(3,7)$, we substitute these coordinates into the equation $3x + 8y = C$, where $C$ is a constant. Substituting $x = 3$ and $y = 7$, we get $3(3) + 8(7) = 9 + 56 = 65$. Therefore, the equation of the line is $3x + 8y = 65$, which is in standard form.

Question 20

Write all linear equations in slope-intercept form.
-A biologist recorded 6 snakes on 16 acres in one area and 15 snakes on 33 acres in another area. Find a linear equation that models the number of snakes in x acres.

Accepted Answer

The answer of Write all linear equations in slope-intercept form.
-A...

Quiz 3: Graphs and Functions

Write an equation for the line described. Write the equation in the form specified. -parallel to $2 x + 7 y = 65$ , through $( 8,4 )$ ; slope-intercept form

Write an equation for the line described. Write the equation in the form specified. -parallel to $x = - 2$ , through $( 5,3 )$

Write all linear equations in slope-intercept form. -With 23.5% commitment, a company can clean up 40% of an energy leak. With 28.5% commitment, it can clean up 80% of an energy leak. Find a linear equation that models the percent cleanup for x percent commitment.

Write an equation for the line described. Write the equation in the form specified. -perpendicular to $y = 2$ , through $( 3,4 )$

Write all linear equations in slope-intercept form. -A company can make 9 satellite dishes for $92,300, while 16 satellite dishes cost $97,130. Find a linear equation that models the cost to produce x satellite dishes.

Write an equation for the line described. Write the equation in the form specified. -perpendicular to $x = - 3$ , through $( 8,7 )$

Write an equation for the line described. Write the equation in the form specified. -perpendicular to $2 x - 5 y = - 19$ , through $( 3 , - 5 )$ ; slope-intercept form

Write an equation for the line described. Write the equation in the form specified. -parallel to $\mathrm { y } = - 9$ , through $( 5,3 )$

Write all linear equations in slope-intercept form. -A house was purchased for $83,000. After 6 years the value of the house was $101,000. Find a linear equation that models the value of the house after x years.

Write an equation for the line described. Write the equation in the form specified. -parallel to $y + 8 x = 4$ , through $( 4,5 )$ ; slope-intercept form

The graph of a linear function f is shown. Write the equation that defines f. Write the equation in slope-intercept form. -

Write an equation for the line described. Write the equation in the form specified. -perpendicular to $8 x - 7 y = 127$ , through $( 8,9 )$ ; standard form

Write an equation for the line described. Write the equation in the form specified. -perpendicular to $- 2 x + y = 8$ , through $( 5,4 )$ ; slope-intercept form

Write all linear equations in slope-intercept form. -In a lab experiment 3 grams of acid were produced in 17 minutes and 18 grams in 45 minutes. Find a linear equation that models the number of grams produced in x minutes.

Write an equation for the line described. Write the equation in the form specified. -parallel to $3 x + 8 y = 57$ ; through $( 3,7 )$ ; standard form

Write all linear equations in slope-intercept form. -A biologist recorded 6 snakes on 16 acres in one area and 15 snakes on 33 acres in another area. Find a linear equation that models the number of snakes in x acres.

Quiz 3: Graphs and Functions

Write an equation for the line described. Write the equation in the form specified. -parallel to 2x+7y=652 x + 7 y = 652x+7y=65 , through (8,4) ( 8,4 ) (8,4) ; slope-intercept form

Write an equation for the line described. Write the equation in the form specified. -parallel to x=−2x = - 2x=−2 , through (5,3) ( 5,3 ) (5,3)

Write all linear equations in slope-intercept form. -With 23.5% commitment, a company can clean up 40% of an energy leak. With 28.5% commitment, it can clean up 80% of an energy leak. Find a linear equation that models the percent cleanup for x percent commitment.

Write an equation for the line described. Write the equation in the form specified. -perpendicular to y=2y = 2y=2 , through (3,4) ( 3,4 ) (3,4)

Write all linear equations in slope-intercept form. -A company can make 9 satellite dishes for $92,300, while 16 satellite dishes cost $97,130. Find a linear equation that models the cost to produce x satellite dishes.

Write an equation for the line described. Write the equation in the form specified. -perpendicular to x=−3x = - 3x=−3 , through (8,7) ( 8,7 ) (8,7)

Write an equation for the line described. Write the equation in the form specified. -perpendicular to 2x−5y=−192 x - 5 y = - 192x−5y=−19 , through (3,−5) ( 3 , - 5 ) (3,−5) ; slope-intercept form

Write an equation for the line described. Write the equation in the form specified. -parallel to y=−9\mathrm { y } = - 9y=−9 , through (5,3) ( 5,3 ) (5,3)

Write all linear equations in slope-intercept form. -A house was purchased for $83,000. After 6 years the value of the house was $101,000. Find a linear equation that models the value of the house after x years.

Write an equation for the line described. Write the equation in the form specified. -parallel to y+8x=4y + 8 x = 4y+8x=4 , through (4,5) ( 4,5 ) (4,5) ; slope-intercept form

The graph of a linear function f is shown. Write the equation that defines f. Write the equation in slope-intercept form. -

Write an equation for the line described. Write the equation in the form specified. -perpendicular to 8x−7y=1278 x - 7 y = 1278x−7y=127 , through (8,9) ( 8,9 ) (8,9) ; standard form

Write an equation for the line described. Write the equation in the form specified. -perpendicular to −2x+y=8- 2 x + y = 8−2x+y=8 , through (5,4) ( 5,4 ) (5,4) ; slope-intercept form

Write all linear equations in slope-intercept form. -In a lab experiment 3 grams of acid were produced in 17 minutes and 18 grams in 45 minutes. Find a linear equation that models the number of grams produced in x minutes.

Write an equation for the line described. Write the equation in the form specified. -parallel to 3x+8y=573 x + 8 y = 573x+8y=57 ; through (3,7) ( 3,7 ) (3,7) ; standard form

Write all linear equations in slope-intercept form. -A biologist recorded 6 snakes on 16 acres in one area and 15 snakes on 33 acres in another area. Find a linear equation that models the number of snakes in x acres.

Write an equation for the line described. Write the equation in the form specified. -parallel to $2 x + 7 y = 65$ , through $( 8,4 )$ ; slope-intercept form

Write an equation for the line described. Write the equation in the form specified. -parallel to $x = - 2$ , through $( 5,3 )$

Write an equation for the line described. Write the equation in the form specified. -perpendicular to $y = 2$ , through $( 3,4 )$

Write an equation for the line described. Write the equation in the form specified. -perpendicular to $x = - 3$ , through $( 8,7 )$

Write an equation for the line described. Write the equation in the form specified. -perpendicular to $2 x - 5 y = - 19$ , through $( 3 , - 5 )$ ; slope-intercept form

Write an equation for the line described. Write the equation in the form specified. -parallel to $\mathrm { y } = - 9$ , through $( 5,3 )$

Write an equation for the line described. Write the equation in the form specified. -parallel to $y + 8 x = 4$ , through $( 4,5 )$ ; slope-intercept form

Write an equation for the line described. Write the equation in the form specified. -perpendicular to $8 x - 7 y = 127$ , through $( 8,9 )$ ; standard form

Write an equation for the line described. Write the equation in the form specified. -perpendicular to $- 2 x + y = 8$ , through $( 5,4 )$ ; slope-intercept form

Write an equation for the line described. Write the equation in the form specified. -parallel to $3 x + 8 y = 57$ ; through $( 3,7 )$ ; standard form