Question 1

Write an equation of the line passing through the given points. Write the equation in standard form Ax + By = C.
- (2,-4)  and  (0,5) 
A)  -9x+2y=10 
B)  -6x+5y=-25 
C)  9x+2y=10 
D)  6x-5y=-25

Accepted Answer

The slope of the line is (5 - (-4)) / (0 - 2) = 9 / -2 = -9/2. Using point-slope form with point (0,5), y - 5 = -9/2(x - 0), which simplifies to y = -9/2x + 5. Converting to standard form: 9x + 2y = 10.

Question 2

Use the slope-intercept form of the linear equation to write the equation of the line with the given slope and y-intercept.
-Slope $\frac { 1 } { 3 } ; \mathrm { y }$-intercept $( 0,4 )$
A) $y = - \frac { 1 } { 3 } x + 4$
B) $y = \frac { 1 } { 3 } x - 4$
C) $y = \frac { 1 } { 3 } x + 4$
D) $y = - \frac { 1 } { 3 } x - 4$

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. Given a slope of $\frac{1}{3}$ and a y-intercept of 4, the equation is $y = \frac{1}{3}x + 4$.

Question 3

Write an equation of the line with the given slope and containing the given point. Write the equation in the
slope-intercept form y = mx + b.
-Slope $\frac { 6 } { 7 }$ ; through  (0,6) 
A)  y=$\frac { 6 } { 7 }$x+6 
B)  y=-$\frac { 6 } { 7 }$x-6 
C)  y=$\frac { 7 } { 6 }$x+7 
D)  y=$\frac { 6 } { 7 }$x-6

Accepted Answer

The slope-intercept form of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept. Given the slope $\frac{6}{7}$ and that the line passes through the point (0,6), the y-intercept $b$ is 6. Therefore, the equation of the line is $y = \frac{6}{7}x + 6$.

Question 4

Use the slope-intercept form of the linear equation to write the equation of the line with the given slope and y-intercept.
-Slope $\frac { 2 } { 3 } ; y$-intercept $( 0 , - 7 )$
A) $y = - \frac { 3 } { 2 } x + 7$
B) $y = \frac { 2 } { 3 } x - 7$
C) $y = - \frac { 3 } { 2 } x - 7$
D) $y = \frac { 2 } { 3 } x + 7$

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. Given the slope $\frac{2}{3}$ and y-intercept $-7$, the equation is $y = \frac{2}{3}x - 7$.

Question 5

Use the slope-intercept form of the linear equation to write the equation of the line with the given slope and y-intercept.
-Slope $- \frac { 3 } { 7 } ; y$-intercept $( 0,0 )$
A) $y = - \frac { 3 } { 7 }$
B) $y = - \frac { 3 } { 7 } x$
C) $y = \frac { 3 } { 7 } x$
D) $y = \frac { 3 } { 7 }$

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. Given the slope $- \frac { 3 } { 7 }$ and y-intercept $0$, the equation is $y = - \frac { 3 } { 7 } x$.

Question 6

Write an equation of the line passing through the given points. Write the equation in standard form Ax + By = C.
- (-4,3)  and  (1,-1) 
A)  -7 x+2y=5 
B)  7 x-2y=5 
C)  -4 x-5y=1 
D)  4 x-5y=1

Accepted Answer

The answer of Write an equation of the line passing...

Question 7

Interpret the linear equation.
-The speed of a ball dropped from a tower is given by the linear function y = 32x where y is in feet per second and x is the number of seconds since the ball was dropped. Find and interpret the slope and y-intercept of the
Linear equation.
A) m = 32; The speed of the ball increases 32 feet per second every second. There is no y-intercept to interpret.
B) m = 32; The speed of the ball is 32 feet per second. b = 0; When the ball is dropped at x = 0, the ball has fallen 0 feet.
C) m = 32; The speed of the ball increases 32 feet per second every second. b = 0; The speed of the ball was 0 the moment it was dropped.
D) m = 0; The speed of the ball does not increase as time passes. b = 32; At time x = 0, the ball has fallen 32 feet.

Accepted Answer

The slope (m = 32) represents the acceleration due to gravity, indicating the speed of the ball increases by 32 feet per second for each second it falls. The y-intercept (b = 0) indicates that at time x = 0 (when the ball is just dropped), its speed is 0 feet per second.

Question 8

Write an equation of the line passing through the given points. Write the equation in standard form Ax + By = C.
-$\left( \frac { 5 } { 4 } , - \frac { 5 } { 4 } \right) \text { and } \left( - \frac { 4 } { 3 } , - \frac { 5 } { 3 } \right)$
A)  5 x-31y=45 
B)  -31 x+5y=45 
C)  5 x-31y=-45 
D)  -5 x+31y=45

Accepted Answer

The equation of the line passing through the given points can be found using the slope-intercept form: y = mx + b, where m is the slope and b is the y-intercept. To find the slope, we use the formula: m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two given points. Plugging in the values, we get: m = (-5/3 - (-5/4)) / (-4/3 - 5/4) = 5/31. To find the y-intercept, we can use the point-slope form: y - y1 = m(x - x1), where (x1, y1) is one of the given points. Plugging in the values, we get: y - (-5/4) = 5/31(x - 5/4). Simplifying, we get: y = 5/31x - 5/4 + 5/4 = 5/31x. Converting to standard form, we get: 5x - 31y = 0.

Question 9

Write an equation of the line passing through the given points. Write the equation in standard form Ax + By = C.
- (-4,0)  and  (9,-3) 
A)  -3 x-13y=12 
B)  4 x-12y=0 
C)  3 x-13y=12 
D)  -4 x+12y=0

Accepted Answer

The slope of the line passing through the points (-4,0) and (9,-3) is -3/13. The equation of the line in standard form is Ax + By = C, where A, B, and C are integers. Substituting the slope and one of the points into the equation, we get -3x + 13y = C. To find the value of C, we substitute the other point into the equation: -3(9) + 13(-3) = C, which gives C = 12. Therefore, the equation of the line in standard form is -3x + 13y = 12.

Question 10

Interpret the linear equation.
-The monthly cost of a certain long distance service is given by the linear function y = 0.08x + 3.95 where y is in dollars and x is the amount of time in minutes called in a month. Find and interpret the slope and y-intercept of
The linear equation.
A) m = 3; The number of minutes called in a month increases 3.95 for every dollar spent. b = 0.08; The number of minutes that can be called when x = 0 is 0.08.
B) m = 0.08; The number of minutes called in a month increases 0.08 for every dollar spent. b = 3.95; The number of minutes that can be called when x = 0 is 3.95.
C) m = 3.95; The cost of the long distance service increases $3.95 for every 1 minute called. b = 0.08; The cost of the long distance service is $0.08 if no calls are made for the month.
D) m = 0.08; The cost of the long distance service increases $0.08 for every 1 minute called. b = 3.95; The cost of the long distance service is $3.95 if no calls are made for the month.

Accepted Answer

The slope (m = 0.08) represents the rate at which cost increases per minute of call time, and the y-intercept (b = 3.95) represents the basic monthly cost when no calls are made.

Question 11

Interpret the linear equation.
-The altitude above sea level of an airplane just after taking off from an airport on a high plateau is given by the linear function y = 900x + 3498, where y is in feet and x is the time in minutes since take-off. Find and interpret
The slope and y-intercept.
A) m = 900; The minutes since take-off increases 900 for every foot of altitude. b = 3498; The minutes that the plane takes to get to the altitude of the airport from sea level.
B) m = 3498; The minutes since take-off increases 3498 for every foot of altitude. b = 900; The minutes that the plane takes to get to the altitude of the airport from sea level.
C) m = 900; The altitude of the airplane increases 900 feet every minute. b = 3498; The altitude of the airport where the airplane took-off is 3498 feet above sea level.
D) m = 3498; The altitude of the airplane increases 3498 feet every minute. b = 3498; The altitude of the airport where the airplane took-off is 900 feet above sea level.

Accepted Answer

The slope (m = 900) represents the rate of change of altitude with respect to time, meaning the airplane ascends 900 feet per minute. The y-intercept (b = 3498) represents the initial altitude, indicating the airport is 3498 feet above sea level at takeoff.

Question 12

Write an equation of the line passing through the given points. Write the equation in standard form Ax + By = C.
- (8,-3)  and  (6,-8) 
A)  -5 x+2y=-46 
B)  5 x+2y=-46 
C)  11 x+14y=-178 
D)  -11 x-14y=-178

Accepted Answer

First, find the slope (m) using the formula $m = \frac{y_2 - y_1}{x_2 - x_1}$, which gives $m = \frac{-8 - (-3)}{6 - 8} = \frac{-5}{-2} = \frac{5}{2}$. Then, use point-slope form $y - y_1 = m(x - x_1)$ with one of the points, say (8, -3), to get $y + 3 = \frac{5}{2}(x - 8)$. Multiplying through by 2 to clear the fraction gives $2y + 6 = 5x - 40$, and rearranging to standard form $Ax + By = C$ gives $-5x + 2y = -46$.

Question 13

Write an equation of the line with the given slope and containing the given point. Write the equation in the
slope-intercept form y = mx + b.
-Slope  -2 ; through  (-4,6) 
A)  y=-2x+2 
B)  y=-2x-2 
C)  y-6=mx+4 
D)  y-6=x+4

Accepted Answer

The answer of Write an equation of the line with...

Question 14

Interpret the linear equation.
-The amount of water in a leaky bucket is given by the linear function y = 120 - 11x, where y is in ounces and x is in minutes. Find and interpret the slope and y-intercept of the linear equation.
A) m = 120; The amount of water in the bucket increases 120 ounces every minute. b = 11; At x = 0, the amount of water in the bucket was 11 ounces.
B) m = 120; The amount of water in the bucket decreases 120 ounces every minute. b = 11; At x = 0, the amount of water in the bucket was 11 ounces.
C) m = -11; The amount of water in the bucket decreases 11 ounces every minute. b = 120; At x = 0, the amount of water in the bucket was 120 ounces.
D) m = 11; The amount of water in the bucket increases 11 ounces every minute. b = 120; At x = 0 the amount of water in the bucket was 120 ounces.

Accepted Answer

The slope (m) of the equation y = 120 - 11x is -11, which indicates the rate of change of water in the bucket is a decrease of 11 ounces per minute. The y-intercept (b) is 120, meaning at x = 0 (the start), the bucket had 120 ounces of water.

Question 15

Use the slope-intercept form of the linear equation to write the equation of the line with the given slope and y-intercept.
-Slope 4; $\mathrm { y }$-intercept $( 0 , - 1 )$
A) $y = - \frac { 1 } { 4 } x - 1$
B) $y = 4 x + 1$
C) $y = - \frac { 1 } { 4 } x + 1$
D) $y = 4 x - 1$

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. Given a slope of 4 and a y-intercept of -1, the equation is $y = 4x - 1$.

Question 16

Find an equation of the line. Write the equation in standard form.
-Slope 0 ; through  (-3,-2) 
A)  x=-3 
B)  y=-3 
C)  x=-2 
D)  y=-2

Accepted Answer

A line with a slope of 0 is horizontal, meaning its y-value is constant. Since the line passes through (-3, -2), the equation is y = -2.

Question 17

Use the slope-intercept form of the linear equation to write the equation of the line with the given slope and y-intercept.
-Slope -4; y-intercept $( 0,9 )$
A) $y = - 4 x + 9$
B) $y = - 9 x + 4$
C) $y = 9 x - 4$
D) $y = 4 x - 9$

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. Given a slope of -4 and a y-intercept of 9, the equation is $y = -4x + 9$.

Question 18

Interpret the linear equation.
-When a tow truck is called, the cost of the service is given by the linear function y = 2x + 55, where y is in dollars and x is the number of miles the car is towed. Find and interpret the slope and y-intercept of the linear
Equation.
A) m = 55; The cost of the service increases $55 every mile the car is towed. b = 2; The cost of the service is $2 if the car is not towed.
B) m = 2; The number of miles the car is towed increases 2 miles for every dollar spent on the service. b = 55; The tow truck will tow the car 55 miles for no cost.
C) m = 2; The cost of the service increases $2 every mile the car is towed. b = 55; The cost of the service is $55 if the car is not towed.
D) m = 55; The number of miles the car is towed increases 55 miles for every dollar spent on the service. b = 2; The tow truck will tow the car 2 miles for no cost.

Accepted Answer

The slope (m = 2) represents the rate of change, indicating the cost increases by $2 for every additional mile towed. The y-intercept (b = 55) represents the initial cost of the service when no miles are towed.

Question 19

Write an equation of the line with the given slope and containing the given point. Write the equation in the
slope-intercept form y = mx + b.
-Slope -$\frac { 3 } { 5 }$ ; through  (2,4) 
A) $y = \frac { 3 } { 5 } x - \frac { 26 } { 5 }$
B) $y = \frac { 3 } { 5 } x + \frac { 26 } { 5 }$
C) $y = - \frac { 3 } { 5 } x + \frac { 26 } { 5 }$
D) $y = - \frac { 3 } { 5 } x - \frac { 26 } { 5 }$

Accepted Answer

The slope-intercept form is $y = mx + b$. Given the slope $m = -\frac{3}{5}$ and point (2,4), substitute into the equation: $4 = -\frac{3}{5}(2) + b$. Solving for $b$, we get $b = \frac{26}{5}$. Thus, the equation is $y = -\frac{3}{5}x + \frac{26}{5}$.

Question 20

Write an equation of the line with the given slope and containing the given point. Write the equation in the
slope-intercept form y = mx + b.
-Slope 3; through  (-4,-2) 
A)  y=3x-10 
B)  y+2=mx+4 
C)  y+2=x+4 
D)  y=3x+10

Accepted Answer

The answer of Write an equation of the line with...

Quiz 3: Graphs and Functions

Write an equation of the line passing through the given points. Write the equation in standard form Ax + By = C. - (2,-4) and (0,5)

Use the slope-intercept form of the linear equation to write the equation of the line with the given slope and y-intercept. -Slope $\frac { 1 } { 3 } ; \mathrm { y }$ -intercept $( 0,4 )$

Write an equation of the line with the given slope and containing the given point. Write the equation in the slope-intercept form y = mx + b. -Slope $\frac { 6 } { 7 }$ ; through (0,6)

Use the slope-intercept form of the linear equation to write the equation of the line with the given slope and y-intercept. -Slope $\frac { 2 } { 3 } ; y$ -intercept $( 0 , - 7 )$

Use the slope-intercept form of the linear equation to write the equation of the line with the given slope and y-intercept. -Slope $- \frac { 3 } { 7 } ; y$ -intercept $( 0,0 )$

Write an equation of the line passing through the given points. Write the equation in standard form Ax + By = C. - (-4,3) and (1,-1)

Interpret the linear equation. -The speed of a ball dropped from a tower is given by the linear function y = 32x where y is in feet per second and x is the number of seconds since the ball was dropped. Find and interpret the slope and y-intercept of the Linear equation.

Write an equation of the line passing through the given points. Write the equation in standard form Ax + By = C. - $\left( \frac { 5 } { 4 } , - \frac { 5 } { 4 } \right) \text { and } \left( - \frac { 4 } { 3 } , - \frac { 5 } { 3 } \right)$

Write an equation of the line passing through the given points. Write the equation in standard form Ax + By = C. - (-4,0) and (9,-3)

Interpret the linear equation. -The monthly cost of a certain long distance service is given by the linear function y = 0.08x + 3.95 where y is in dollars and x is the amount of time in minutes called in a month. Find and interpret the slope and y-intercept of The linear equation.

Interpret the linear equation. -The altitude above sea level of an airplane just after taking off from an airport on a high plateau is given by the linear function y = 900x + 3498, where y is in feet and x is the time in minutes since take-off. Find and interpret The slope and y-intercept.

Write an equation of the line passing through the given points. Write the equation in standard form Ax + By = C. - (8,-3) and (6,-8)

Write an equation of the line with the given slope and containing the given point. Write the equation in the slope-intercept form y = mx + b. -Slope -2 ; through (-4,6)

Interpret the linear equation. -The amount of water in a leaky bucket is given by the linear function y = 120 - 11x, where y is in ounces and x is in minutes. Find and interpret the slope and y-intercept of the linear equation.

Use the slope-intercept form of the linear equation to write the equation of the line with the given slope and y-intercept. -Slope 4; $\mathrm { y }$ -intercept $( 0 , - 1 )$

Find an equation of the line. Write the equation in standard form. -Slope 0 ; through (-3,-2)

Use the slope-intercept form of the linear equation to write the equation of the line with the given slope and y-intercept. -Slope -4; y-intercept $( 0,9 )$

Interpret the linear equation. -When a tow truck is called, the cost of the service is given by the linear function y = 2x + 55, where y is in dollars and x is the number of miles the car is towed. Find and interpret the slope and y-intercept of the linear Equation.

Write an equation of the line with the given slope and containing the given point. Write the equation in the slope-intercept form y = mx + b. -Slope - $\frac { 3 } { 5 }$ ; through (2,4)

Write an equation of the line with the given slope and containing the given point. Write the equation in the slope-intercept form y = mx + b. -Slope 3; through (-4,-2)