Question 1

Write an equation for the line described. Write the equation in the form specified.
-parallel to $5 x + 2 y = 43$; through $( 5,15 )$; standard form
A) $5 x + 2 y = 55$
B) $5 x + 2 y = 43$
C) $5 x - 2 y = 55$
D) $2 x + 5 y = 15$

Accepted Answer

Lines that are parallel have the same slope, meaning their coefficients for x and y will be the same in standard form. The given line is $5x + 2y = 43$. To find a line parallel to it that passes through (5,15), we substitute x and y into the equation $5x + 2y = C$, where C is a constant we need to find. Substituting (5,15) gives $5(5) + 2(15) = 25 + 30 = 55$, so the equation is $5x + 2y = 55$.

Question 2

Solve the problem. Write all linear equations in slope-intercept form.
-By reading a graph on defense spending in the country of Warpeas, you discover that in year 0 the country spent $144 million on defense and in year 8 spent $528 million. Write a linear function that
Relates y (in millions of dollars) to x. 
A) $y = - 48 x - 144$
B) $y = 84 x + 144$
C) $y = 48 x + 144$
D) $y = \frac { 1 } { 3 } x + 144$

Accepted Answer

The slope (m) is calculated as the change in spending over the change in years: $m = \frac{528 - 144}{8 - 0} = 48$. The y-intercept (b) is the initial spending, $144 million. Thus, the equation is $y = 48x + 144$.

Question 3

Solve the problem. Write all linear equations in slope-intercept form.
-A company can make 10 airplane engines for $\$ 123,400$, while 25 airplane engines cost $\$ 133,000$. Find a linear equation that models the cost to produce $x$ airplane engines.
A) $y = x + 9600$
B) $y = 640 x - 117,000$
C) $y = 640 x + 117,000$
D) $y = 15 x + 9600$

Accepted Answer

The answer of Solve the problem. Write all linear equations...

Question 4

Write an equation for the line described. Write the equation in the form specified.
-parallel to $- 5 x + 7 y = 54$, through $( - 8,0 )$; slope-intercept form
A) $y = \frac { 8 } { 7 } x + \frac { 54 } { 7 }$
B) $\mathrm { y } = \frac { 5 } { 7 } \mathrm { x } + \frac { 40 } { 7 }$
C) $y = \frac { 7 } { 5 } x + 0$
D) $y = - \frac { 5 } { 7 } x - \frac { 40 } { 7 }$

Accepted Answer

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

Question 5

Write an equation for the line described. Write the equation in the form specified.
-perpendicular to x = 6, through (3, 5)
A) y = 3
B)x = 3
C)x = 5
D)y = 5

Accepted Answer

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

Question 6

Write an equation for the line described. Write the equation in the form specified.
-perpendicular to -6x + y = 9, through (2, 5); slope-intercept form 
A) $y = - \frac { 1 } { 6 } x - \frac { 16 } { 3 }$
B) $y = - \frac { 1 } { 6 } x + \frac { 16 } { 3 }$
C) $y = - 6 x - 32$
D) $y = \frac { 1 } { 6 } x - \frac { 16 } { 3 }$

Accepted Answer

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

Question 7

Solve the problem. Write all linear equations in slope-intercept form.
-A house was purchased for $\$ 84,000$. After 7 years the value of the house was $\$ 147,000$. Find a linear equation that models the value of the house after $x$ years.
A) $y = 147,000$
B) $y = 7 x + 84,000$
C) $\mathrm { y } = 9000 \mathrm { x }$
D) $y = 9000 x + 84,000$

Accepted Answer

The slope ($m$) of the line is calculated by the change in value over the years, which is $(147,000 - 84,000) / 7 = 9,000$. The y-intercept ($b$) is the initial value, $84,000$. Thus, the equation is $y = 9000x + 84,000$.

Question 8

Solve the problem. 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 735 mL container takes 13 seconds to go out and a flame in
A) 1225 mL container takes 23 seconds. Write a linear function that relates t to x. A) $t = \frac { 1 } { 49 } x - 2$
B) $t = \frac { 1 } { 49 } x$
C) $t = 49 x - 2$
D) $t = \frac { 9 } { 490 } x - \frac { 1 } { 2 }$

Accepted Answer

To find the correct linear function, we use the two given points: (735, 13) and (1225, 23). The slope $m$ of the line is calculated as $\frac{23 - 13}{1225 - 735} = \frac{10}{490} = \frac{1}{49}$. Using one of the points to solve for the y-intercept $b$, $13 = \frac{1}{49} \cdot 735 + b$, we find $b = -2$. Thus, the equation is $t = \frac{1}{49}x - 2$.

Question 9

Write an equation for the line described. Write the equation in the form specified.
-perpendicular to $7 x - 6 y = 2$, through $( 8 , - 9 )$; standard form
A) $6 x - 7 y = - 15$
B) $8 x + 6 y = 2$
C) $6 x + 7 y = - 15$
D) $7 x + 6 = 7$

Accepted Answer

The slope of the line $7x - 6y = 2$ is $\frac{7}{6}$. A line perpendicular to it will have a slope of $-\frac{6}{7}$. Using the point-slope form with point $(8, -9)$, the equation is $y + 9 = -\frac{6}{7}(x - 8)$. Converting to standard form gives $6x + 7y = -15$.

Question 10

Solve the problem. 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.

Determine a linear function f defined by f(x) = mx + b that models the data using (1, 1340) and (6, 3045).
A) $f ( x ) = 1340$
B) $f ( x ) = 2781 - 1441 x$
C) $f ( x ) = 999 x + 341$
D) $f ( x ) = 341 x + 999$

Accepted Answer

The answer of Solve the problem. Write all linear equations...

Question 11

Write an equation for the line described. Write the equation in the form specified.
-perpendicular to $4 x - 5 y = 24$, through $( 1,4 )$; slope-intercept form
A) $y = - \frac { 1 } { 5 } x + \frac { 24 } { 5 }$
B) $y = - \frac { 4 } { 5 } x - \frac { 4 } { 5 }$
C) $y = - \frac { 5 } { 4 } x + \frac { 21 } { 4 }$
D) $y = \frac { 5 } { 4 } x + \frac { 21 } { 4 }$

Accepted Answer

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

Question 12

Solve the problem. Write all linear equations in slope-intercept form.
-In a lab experiment 6 grams of acid were produced in 21 minutes and 18 grams in 31 minutes. Find a linear equation that models the number of grams produced in $x$ minutes.
A) $y = \frac { 6 } { 5 } x + \frac { 96 } { 5 }$
B) $y = \frac { 6 } { 5 } x - \frac { 96 } { 5 }$
C) $y = x + 15$
D) $y = \frac { 5 } { 6 } x - \frac { 5 } { 96 }$

Accepted Answer

The slope of the line is calculated using the points (21, 6) and (31, 18), which gives a slope of $\frac{6}{5}$. Using the point-slope form and converting to slope-intercept form, the equation is $y = \frac{6}{5}x - \frac{96}{5}$.

Question 13

Solve the problem. Write all linear equations in slope-intercept form.
-A driver wants to gauge the fuel efficiency of her vehicle at speeds of $30 \mathrm { mph }$ and above. She notices that traveling at an average speed of $40 \mathrm { mph }$ results in a rating of $36 \mathrm { mpg }$, whereas at an average speed of $45 \mathrm { mph }$, her car rates $21 \mathrm { mpg }$. Find a linear equation to model the gas mileage y for an average speed of $x \mathrm { mph }$. Find the slope-intercept form of the equation of the line.
A) $y = - 3 x + 156$
B) $y = \frac { 1 } { 3 } x + 156$
C) $y = \frac { 1 } { 3 } x + 84$
D) $y = - 3 x + 84$

Accepted Answer

The slope $m$ of the line can be calculated using the two given points $(40, 36)$ and $(45, 21)$ as $m = \frac{21 - 36}{45 - 40} = \frac{-15}{5} = -3$. Using the point-slope form $y - y_1 = m(x - x_1)$ with one of the points, for example, $(40, 36)$, we get $y - 36 = -3(x - 40)$. Simplifying this equation to slope-intercept form $y = mx + b$ gives $y = -3x + 156$.

Question 14

Use a graphing calculator to solve the linear equation.
-$$- 8 x + 3 + 6 x = - 2 x + 8$$
A) $\{ 5 \}$
B) $\{ - 3 \}$
C) all real numbers
D) $\varnothing$

Accepted Answer

The answer of Use a graphing calculator to solve the...

Question 15

Solve the problem. Write all linear equations in slope-intercept form.
-A biologist recorded 2 snakes on 14 acres in one area and 20 snakes on 31 acres in another area. Find a linear equation that models the number of snakes in $\mathrm { x }$ acres.
A) $y = \frac { 18 } { 17 } x + \frac { 218 } { 17 }$
B) $y = x + 12$
C) $y = \frac { 18 } { 17 } x - \frac { 218 } { 17 }$
D) $y = \frac { 17 } { 18 } x - \frac { 17 } { 218 }$

Accepted Answer

To find the linear equation that models the number of snakes in $x$ acres, we use the two points given: (14, 2) and (31, 20). The slope $m$ of the line is calculated as $\frac{20 - 2}{31 - 14} = \frac{18}{17}$. 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 (14, 2), we get $2 = \frac{18}{17} \cdot 14 + b$, solving for $b$ gives $b = -\frac{218}{17}$. Thus, the equation is $y = \frac{18}{17}x - \frac{218}{17}$.

Question 16

Write an equation for the line described. Write the equation in the form specified.
-perpendicular to $\mathrm { y } = - 5$, through $( 7,3 )$
A) $y = 3$
B) $y = 7$
C) $x = 7$
D) $x = 3$

Accepted Answer

A line perpendicular to $y = -5$ (a horizontal line) is a vertical line. A vertical line passing through $(7,3)$ has the equation $x = 7$.

Question 17

Solve the problem. Write all linear equations in slope-intercept form.
-With $31.5 \%$ commitment, a company can clean up $40 \%$ of an oil spill. With $35.5 \%$ commitment, it can clean up $72 \%$ of an oil spill. Find a linear equation that models the percent cleanup for $x$ percent commitment.
A) $y = x + 32$
B) $y = 8 x - 212$
C) $y = 4 x + 32$
D) $y = 8 x + 212$

Accepted Answer

To find the linear equation, we use the given points (31.5, 40) and (35.5, 72) to calculate the slope $m = \frac{72 - 40}{35.5 - 31.5} = \frac{32}{4} = 8$. Then, using point-slope form $y - y_1 = m(x - x_1)$ with one of the points, say (31.5, 40), we get $y - 40 = 8(x - 31.5)$. Simplifying, $y = 8x - 8(31.5) + 40 = 8x - 252 + 40 = 8x - 212$, which matches option B.

Question 18

Solve the problem. Write all linear equations in slope-intercept form.
-Suppose that a sales person observes that if an item is priced at $\$ 3$ per item then 7 items are sold. If 5 items are sold for $\$ 5$ 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.
A) $y = - x + 4$
B) $y = - x + 10$
C) $y = x + 10$
D) $y = x + 4$

Accepted Answer

The slope $m$ of the line can be found using the two given points $(3,7)$ and $(5,5)$ as $m = \frac{5-7}{5-3} = \frac{-2}{2} = -1$. The slope-intercept form is $y = mx + b$. Using the point $(3,7)$, we can solve for $b$: $7 = -1(3) + b$, leading to $b = 10$. Thus, the equation is $y = -x + 10$.

Question 19

Write an equation for the line described. Write the equation in the form specified.
-parallel to $y + 6 x = 4$, through $( 4,5 )$; slope-intercept form
A) $y = - 6 x - 29$
B) $y = - \frac { 1 } { 6 } x - \frac { 29 } { 6 }$
C) $y = 6 x - 29$
D) $y = - 6 x + 29$

Accepted Answer

Parallel lines have the same slope. The given equation $y + 6x = 4$ can be rewritten in slope-intercept form as $y = -6x + 4$, indicating a slope of $-6$. For a line parallel to this through $(4,5)$, we use the slope $-6$ and the point to find the y-intercept using $y = mx + b$, where $m = -6$, $x = 4$, and $y = 5$. Solving for $b$, we get $5 = -6(4) + b$, leading to $b = 29$. Thus, the equation is $y = -6x + 29$.

Question 20

Write an equation for the line described. Write the equation in the form specified.
-parallel to $x = - 7$, through $( 2,5 )$
A) $x = 2$
B) $\mathrm { y } = - 7$
C) $x = 5$
D) $y = 5$

Accepted Answer

A line parallel to $x = -7$ is also a vertical line, which means its equation will have the form $x = \text{constant}$. Since it passes through $(2,5)$, the constant is 2, making the equation $x = 2$.

Quiz 2: Graphs and Functions

Write an equation for the line described. Write the equation in the form specified. -parallel to $5 x + 2 y = 43$ ; through $( 5,15 )$ ; standard form

Solve the problem. Write all linear equations in slope-intercept form. -A company can make 10 airplane engines for $\$ 123,400$ , while 25 airplane engines cost $\$ 133,000$ . Find a linear equation that models the cost to produce $x$ airplane engines.

Write an equation for the line described. Write the equation in the form specified. -parallel to $- 5 x + 7 y = 54$ , through $( - 8,0 )$ ; slope-intercept form

Write an equation for the line described. Write the equation in the form specified. -perpendicular to x = 6, through (3, 5)

Write an equation for the line described. Write the equation in the form specified. -perpendicular to -6x + y = 9, through (2, 5) ; slope-intercept form

Solve the problem. Write all linear equations in slope-intercept form. -A house was purchased for $\$ 84,000$ . After 7 years the value of the house was $\$ 147,000$ . Find a linear equation that models the value of the house after $x$ years.

Solve the problem. 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 735 mL container takes 13 seconds to go out and a flame in

Write an equation for the line described. Write the equation in the form specified. -perpendicular to $7 x - 6 y = 2$ , through $( 8 , - 9 )$ ; standard form

Write an equation for the line described. Write the equation in the form specified. -perpendicular to $4 x - 5 y = 24$ , through $( 1,4 )$ ; slope-intercept form

Solve the problem. Write all linear equations in slope-intercept form. -In a lab experiment 6 grams of acid were produced in 21 minutes and 18 grams in 31 minutes. Find a linear equation that models the number of grams produced in $x$ minutes.

Use a graphing calculator to solve the linear equation. - $- 8 x + 3 + 6 x = - 2 x + 8$

Solve the problem. Write all linear equations in slope-intercept form. -A biologist recorded 2 snakes on 14 acres in one area and 20 snakes on 31 acres in another area. Find a linear equation that models the number of snakes in $\mathrm { x }$ acres.

Write an equation for the line described. Write the equation in the form specified. -perpendicular to $\mathrm { y } = - 5$ , through $( 7,3 )$

Solve the problem. Write all linear equations in slope-intercept form. -With $31.5 \%$ commitment, a company can clean up $40 \%$ of an oil spill. With $35.5 \%$ commitment, it can clean up $72 \%$ of an oil spill. 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. -parallel to $y + 6 x = 4$ , through $( 4,5 )$ ; slope-intercept form

Write an equation for the line described. Write the equation in the form specified. -parallel to $x = - 7$ , through $( 2,5 )$

Quiz 2: Graphs and Functions

Write an equation for the line described. Write the equation in the form specified. -parallel to 5x+2y=435 x + 2 y = 435x+2y=43 ; through (5,15) ( 5,15 ) (5,15) ; standard form

Solve the problem. Write all linear equations in slope-intercept form. -A company can make 10 airplane engines for $123,400\$ 123,400$123,400 , while 25 airplane engines cost $133,000\$ 133,000$133,000 . Find a linear equation that models the cost to produce xxx airplane engines.

Write an equation for the line described. Write the equation in the form specified. -parallel to −5x+7y=54- 5 x + 7 y = 54−5x+7y=54 , through (−8,0) ( - 8,0 ) (−8,0) ; slope-intercept form

Write an equation for the line described. Write the equation in the form specified. -perpendicular to x = 6, through (3, 5)

Write an equation for the line described. Write the equation in the form specified. -perpendicular to -6x + y = 9, through (2, 5) ; slope-intercept form

Solve the problem. Write all linear equations in slope-intercept form. -A house was purchased for $84,000\$ 84,000$84,000 . After 7 years the value of the house was $147,000\$ 147,000$147,000 . Find a linear equation that models the value of the house after xxx years.

Solve the problem. 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 735 mL container takes 13 seconds to go out and a flame in

Write an equation for the line described. Write the equation in the form specified. -perpendicular to 7x−6y=27 x - 6 y = 27x−6y=2 , 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 4x−5y=244 x - 5 y = 244x−5y=24 , through (1,4) ( 1,4 ) (1,4) ; slope-intercept form

Solve the problem. Write all linear equations in slope-intercept form. -In a lab experiment 6 grams of acid were produced in 21 minutes and 18 grams in 31 minutes. Find a linear equation that models the number of grams produced in xxx minutes.

Use a graphing calculator to solve the linear equation. - −8x+3+6x=−2x+8- 8 x + 3 + 6 x = - 2 x + 8−8x+3+6x=−2x+8

Solve the problem. Write all linear equations in slope-intercept form. -A biologist recorded 2 snakes on 14 acres in one area and 20 snakes on 31 acres in another area. Find a linear equation that models the number of snakes in x\mathrm { x }x acres.

Write an equation for the line described. Write the equation in the form specified. -perpendicular to y=−5\mathrm { y } = - 5y=−5 , through (7,3) ( 7,3 ) (7,3)

Write an equation for the line described. Write the equation in the form specified. -parallel to y+6x=4y + 6 x = 4y+6x=4 , through (4,5) ( 4,5 ) (4,5) ; slope-intercept form

Write an equation for the line described. Write the equation in the form specified. -parallel to x=−7x = - 7x=−7 , through (2,5) ( 2,5 ) (2,5)

Write an equation for the line described. Write the equation in the form specified. -parallel to $5 x + 2 y = 43$ ; through $( 5,15 )$ ; standard form

Solve the problem. Write all linear equations in slope-intercept form. -A company can make 10 airplane engines for $\$ 123,400$ , while 25 airplane engines cost $\$ 133,000$ . Find a linear equation that models the cost to produce $x$ airplane engines.

Write an equation for the line described. Write the equation in the form specified. -parallel to $- 5 x + 7 y = 54$ , through $( - 8,0 )$ ; slope-intercept form

Solve the problem. Write all linear equations in slope-intercept form. -A house was purchased for $\$ 84,000$ . After 7 years the value of the house was $\$ 147,000$ . 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. -perpendicular to $7 x - 6 y = 2$ , through $( 8 , - 9 )$ ; standard form

Write an equation for the line described. Write the equation in the form specified. -perpendicular to $4 x - 5 y = 24$ , through $( 1,4 )$ ; slope-intercept form

Solve the problem. Write all linear equations in slope-intercept form. -In a lab experiment 6 grams of acid were produced in 21 minutes and 18 grams in 31 minutes. Find a linear equation that models the number of grams produced in $x$ minutes.

Use a graphing calculator to solve the linear equation. - $- 8 x + 3 + 6 x = - 2 x + 8$

Solve the problem. Write all linear equations in slope-intercept form. -A biologist recorded 2 snakes on 14 acres in one area and 20 snakes on 31 acres in another area. Find a linear equation that models the number of snakes in $\mathrm { x }$ acres.

Write an equation for the line described. Write the equation in the form specified. -perpendicular to $\mathrm { y } = - 5$ , through $( 7,3 )$

Write an equation for the line described. Write the equation in the form specified. -parallel to $y + 6 x = 4$ , through $( 4,5 )$ ; slope-intercept form

Write an equation for the line described. Write the equation in the form specified. -parallel to $x = - 7$ , through $( 2,5 )$