Question 1

Use the slope-intercept form to graph the equation.
-$6 x+4 y=24$

Accepted Answer

The answer of Use the slope-intercept form to graph the...

Question 2

Use the slope-intercept form to graph the equation.
-$y = - \frac { 1 } { 5 } x + 2$

Accepted Answer

The answer of Use the slope-intercept form to graph the...

Question 3

Find the slopes of the lines that are (a) parallel to and (b) perpendicular to the line passing through the pair of points.
-$( 3 , - 4 )$ and $( 5,10 )$

Accepted Answer

The slope of the line passing through the points $(3, -4)$ and $(5, 10)$ is calculated using the slope formula $m = \frac{y_2 - y_1}{x_2 - x_1}$. Substituting the given points, we get $m = \frac{10 - (-4)}{5 - 3} = \frac{14}{2} = 7$. Lines parallel to this line will have the same slope, so $m_{parallel} = 7$. Lines perpendicular to this line will have a slope that is the negative reciprocal of $7$, so $m_{perpendicular} = -\frac{1}{7}$.

Question 4

Use the slope-intercept form to graph the equation.
-$y = \frac { 1 } { 2 } x + 2$

Accepted Answer

The answer of Use the slope-intercept form to graph the...

Question 5

Use the slope-intercept form to graph the equation.
-$7 x+y=0$

Accepted Answer

The answer of Use the slope-intercept form to graph the...

Question 6

Use the slope-intercept form to graph the equation.
-$y = \frac { 5 } { 6 } x - 5$

Accepted Answer

The answer of Use the slope-intercept form to graph the...

Question 7

Solve.
-An inclined walkway leading to a new building is to rise 10 inches for each horizontal distance of 14 feet. Write this slope as a grade. (Round to the nearest tenth of a percent if necessary.)

Accepted Answer

The answer of Solve.
-An inclined walkway leading to a new...

Question 8

Use the slope-intercept form to graph the equation.
-$y = \frac { 1 } { 3 } x$

Accepted Answer

The answer of Use the slope-intercept form to graph the...

Question 9

Solve.
-The pitch of a roof is its slope. Find the pitch of the roof shown.

Accepted Answer

The answer of Solve.
-The pitch of a roof is its...

Question 10

Use the slope-intercept form to graph the equation.
-$y=-3 x-2$

Accepted Answer

The answer of Use the slope-intercept form to graph the...

Question 11

Determine whether the pair of lines is parallel, perpendicular, or neither.
-$\begin{array} { l } 
6 x + 2 y = 8 \
9 x + 3 y = 14
\end{array}$

Accepted Answer

The slopes of both lines are equal, indicating they are parallel. To see this, rewrite each equation in slope-intercept form (y = mx + b). For the first equation, 2y = -6x + 8, or y = -3x + 4. For the second equation, 3y = -9x + 14, or y = -3x + 14/3. Both have a slope of -3, indicating parallel lines.

Question 12

Use the slope-intercept form to graph the equation.
-$6 x+y=4$

Accepted Answer

The answer of Use the slope-intercept form to graph the...

Question 13

Solve.
-To the nearest dollar, the average tuition at a public four-year college was $\$ 3024$ in 1997 and $\$ 3216$ in 1998. Use the ordered pairs $( 1997 , \$ 3024 )$ and $( 1998 , \$ 3216 )$ to find and interpret the slope of the line representing the change in tuition (to the nearest dollar per year).

Accepted Answer

The slope of the line representing the change in tuition is calculated using the formula $\frac{y_2 - y_1}{x_2 - x_1}$, where $(x_1, y_1)$ and $(x_2, y_2)$ are the given points. Substituting the given values, we get $\frac{3216 - 3024}{1998 - 1997} = \frac{192}{1} = 192$. This means the tuition increased by \$192 per year.

Question 14

Find the slope of the line and write the slope as a rate of change. Don't forget to attach the proper units.
-The graph shows the total cost y (in dollars) of owning and operating a mini-van where x is the number of miles driven.

Accepted Answer

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

Question 15

Solve.
-A section of roller coaster track has the dimensions shown in the diagram. Find the grade of the track, which is the slope written as a percent.

Accepted Answer

The answer of Solve.
-A section of roller coaster track has...

Question 16

Find the slopes of the lines that are (a) parallel to and (b) perpendicular to the line passing through the pair of points.
-$( 3,3 )$ and $( - 4 , - 4 )$

Accepted Answer

The answer of Find the slopes of the lines that...

Question 17

Use the slope-intercept form to graph the equation.
-$6 y=2 x$

Accepted Answer

The answer of Use the slope-intercept form to graph the...

Question 18

Solve.
-The approach ramp used by a daredevil motorcyclist for flying over a collection of flaming barrels of oil has a rise of 13 feet for every 20 feet in horizontal distance. Find the grade of the ramp. Round to the nearest whole percent.

Accepted Answer

The grade of the ramp is calculated as the rise over the run (horizontal distance) times 100 to convert it to a percentage. So, the grade = $(13/20) \times 100 = 65\%$.

Question 19

Determine whether the pair of lines is parallel, perpendicular, or neither.
-$\begin{array} { l } 
4 x - 3 y = 15 \
3 x + 3 y = - 10
\end{array}$

Accepted Answer

To determine the relationship between the two lines, we first convert the equations into slope-intercept form (y = mx + b), where m is the slope. For the first equation, $4x - 3y = 15$, we solve for y to get $y = \frac{4}{3}x - 5$. For the second equation, $3x + 3y = -10$, we solve for y to get $y = -x - \frac{10}{3}$. The slopes are $\frac{4}{3}$ and $-1$, respectively. Since the slopes are neither equal (which would indicate parallel lines) nor negative reciprocals of each other (which would indicate perpendicular lines), the lines are neither parallel nor perpendicular.

Question 20

Determine whether the pair of lines is parallel, perpendicular, or neither.
-$\begin{aligned}
6 x + 2 y & = 8 \
27 x + 9 y & = 38
\end{aligned}$

Accepted Answer

The slopes of both lines are equal, indicating they are parallel. To see this, rewrite each equation in slope-intercept form (y = mx + b). For the first equation, $2y = -6x + 8$, so $y = -3x + 4$. For the second equation, $9y = -27x + 38$, so $y = -3x + \frac{38}{9}$. Both have a slope of -3.

Quiz 3: Graphing

Use the slope-intercept form to graph the equation. - $6 x+4 y=24$

Use the slope-intercept form to graph the equation. - $y = - \frac { 1 } { 5 } x + 2$ $Use the slope-intercept form to graph the equation. - y = - \frac { 1 } { 5 } x + 2 A) B) C) D)$

Find the slopes of the lines that are (a) parallel to and (b) perpendicular to the line passing through the pair of points. - $( 3 , - 4 )$ and $( 5,10 )$

Use the slope-intercept form to graph the equation. - $y = \frac { 1 } { 2 } x + 2$ $Use the slope-intercept form to graph the equation. - y = \frac { 1 } { 2 } x + 2 A) B) C) D)$

Use the slope-intercept form to graph the equation. - $7 x+y=0$

Use the slope-intercept form to graph the equation. - $y = \frac { 5 } { 6 } x - 5$ $Use the slope-intercept form to graph the equation. - y = \frac { 5 } { 6 } x - 5 A) B) C) D)$

Solve. -An inclined walkway leading to a new building is to rise 10 inches for each horizontal distance of 14 feet. Write this slope as a grade. (Round to the nearest tenth of a percent if necessary.)

Use the slope-intercept form to graph the equation. - $y = \frac { 1 } { 3 } x$ $Use the slope-intercept form to graph the equation. - y = \frac { 1 } { 3 } x A) B) C) D)$

Solve. -The pitch of a roof is its slope. Find the pitch of the roof shown. $Solve. -The pitch of a roof is its slope. Find the pitch of the roof shown. A) \frac { 1 } { 3 } B) \frac { 3 } { 2 } C) \frac { 2 } { 3 } D) 96$

Use the slope-intercept form to graph the equation. - $y=-3 x-2$

Determine whether the pair of lines is parallel, perpendicular, or neither. - $\begin{array} { l } 6 x + 2 y = 8 \\9 x + 3 y = 14\end{array}$

Use the slope-intercept form to graph the equation. - $6 x+y=4$

Find the slopes of the lines that are (a) parallel to and (b) perpendicular to the line passing through the pair of points. - $( 3,3 )$ and $( - 4 , - 4 )$

Use the slope-intercept form to graph the equation. - $6 y=2 x$

Solve. -The approach ramp used by a daredevil motorcyclist for flying over a collection of flaming barrels of oil has a rise of 13 feet for every 20 feet in horizontal distance. Find the grade of the ramp. Round to the nearest whole percent.

Determine whether the pair of lines is parallel, perpendicular, or neither. - $\begin{array} { l } 4 x - 3 y = 15 \\3 x + 3 y = - 10\end{array}$

Determine whether the pair of lines is parallel, perpendicular, or neither. - $\begin{aligned}6 x + 2 y & = 8 \\27 x + 9 y & = 38\end{aligned}$

Quiz 3: Graphing

Use the slope-intercept form to graph the equation. - 6x+4y=246 x+4 y=246x+4y=24

Use the slope-intercept form to graph the equation. - y=−15x+2y = - \frac { 1 } { 5 } x + 2y=−51​x+2

Find the slopes of the lines that are (a) parallel to and (b) perpendicular to the line passing through the pair of points. - (3,−4) ( 3 , - 4 ) (3,−4) and (5,10) ( 5,10 ) (5,10)

Use the slope-intercept form to graph the equation. - y=12x+2y = \frac { 1 } { 2 } x + 2y=21​x+2

Use the slope-intercept form to graph the equation. - 7x+y=07 x+y=07x+y=0

Use the slope-intercept form to graph the equation. - y=56x−5y = \frac { 5 } { 6 } x - 5y=65​x−5

Solve. -An inclined walkway leading to a new building is to rise 10 inches for each horizontal distance of 14 feet. Write this slope as a grade. (Round to the nearest tenth of a percent if necessary.)

Use the slope-intercept form to graph the equation. - y=13xy = \frac { 1 } { 3 } xy=31​x

Solve. -The pitch of a roof is its slope. Find the pitch of the roof shown.

Use the slope-intercept form to graph the equation. - y=−3x−2y=-3 x-2y=−3x−2

Determine whether the pair of lines is parallel, perpendicular, or neither. - 6x+2y=89x+3y=14\begin{array} { l } 6 x + 2 y = 8 \\9 x + 3 y = 14\end{array}6x+2y=89x+3y=14​

Use the slope-intercept form to graph the equation. - 6x+y=46 x+y=46x+y=4

Find the slope of the line and write the slope as a rate of change. Don't forget to attach the proper units. -The graph shows the total cost y (in dollars) of owning and operating a mini-van where x is the number of miles driven.

Solve. -A section of roller coaster track has the dimensions shown in the diagram. Find the grade of the track, which is the slope written as a percent.

Find the slopes of the lines that are (a) parallel to and (b) perpendicular to the line passing through the pair of points. - (3,3) ( 3,3 ) (3,3) and (−4,−4) ( - 4 , - 4 ) (−4,−4)

Use the slope-intercept form to graph the equation. - 6y=2x6 y=2 x6y=2x

Solve. -The approach ramp used by a daredevil motorcyclist for flying over a collection of flaming barrels of oil has a rise of 13 feet for every 20 feet in horizontal distance. Find the grade of the ramp. Round to the nearest whole percent.

Determine whether the pair of lines is parallel, perpendicular, or neither. - 4x−3y=153x+3y=−10\begin{array} { l } 4 x - 3 y = 15 \\3 x + 3 y = - 10\end{array}4x−3y=153x+3y=−10​

Determine whether the pair of lines is parallel, perpendicular, or neither. - 6x+2y=827x+9y=38\begin{aligned}6 x + 2 y & = 8 \\27 x + 9 y & = 38\end{aligned}6x+2y27x+9y​=8=38​

Use the slope-intercept form to graph the equation. - $6 x+4 y=24$

Use the slope-intercept form to graph the equation. - $y = - \frac { 1 } { 5 } x + 2$ $Use the slope-intercept form to graph the equation. - y = - \frac { 1 } { 5 } x + 2 A) B) C) D)$

Find the slopes of the lines that are (a) parallel to and (b) perpendicular to the line passing through the pair of points. - $( 3 , - 4 )$ and $( 5,10 )$

Use the slope-intercept form to graph the equation. - $y = \frac { 1 } { 2 } x + 2$ $Use the slope-intercept form to graph the equation. - y = \frac { 1 } { 2 } x + 2 A) B) C) D)$

Use the slope-intercept form to graph the equation. - $7 x+y=0$

Use the slope-intercept form to graph the equation. - $y = \frac { 5 } { 6 } x - 5$ $Use the slope-intercept form to graph the equation. - y = \frac { 5 } { 6 } x - 5 A) B) C) D)$

Use the slope-intercept form to graph the equation. - $y = \frac { 1 } { 3 } x$ $Use the slope-intercept form to graph the equation. - y = \frac { 1 } { 3 } x A) B) C) D)$

Solve. -The pitch of a roof is its slope. Find the pitch of the roof shown. $Solve. -The pitch of a roof is its slope. Find the pitch of the roof shown. A) \frac { 1 } { 3 } B) \frac { 3 } { 2 } C) \frac { 2 } { 3 } D) 96$

Use the slope-intercept form to graph the equation. - $y=-3 x-2$

Determine whether the pair of lines is parallel, perpendicular, or neither. - $\begin{array} { l } 6 x + 2 y = 8 \\9 x + 3 y = 14\end{array}$

Use the slope-intercept form to graph the equation. - $6 x+y=4$

Find the slopes of the lines that are (a) parallel to and (b) perpendicular to the line passing through the pair of points. - $( 3,3 )$ and $( - 4 , - 4 )$

Use the slope-intercept form to graph the equation. - $6 y=2 x$

Determine whether the pair of lines is parallel, perpendicular, or neither. - $\begin{array} { l } 4 x - 3 y = 15 \\3 x + 3 y = - 10\end{array}$

Determine whether the pair of lines is parallel, perpendicular, or neither. - $\begin{aligned}6 x + 2 y & = 8 \\27 x + 9 y & = 38\end{aligned}$