Question 1

y -intercept - 10 and  x -intercept  -9 
A) $y = \frac { 9 } { 10 } x - 9$
B) $y = - \frac { 9 } { 10 } x - 9$
C) $y = \frac { 10 } { 9 } x - 10$
D) $y = - \frac { 10 } { 9 } x - 10$

Accepted Answer

The y-intercept is -10, and the x-intercept is -9, which matches the equation $y = - \frac { 10 } { 9 } x - 10$.

Question 2

Write the slope-intercept form of the equation for the line passing through the given pair of points.
-$( - 5 , - 3 )$ and $( - 1 , - 6 )$
A) $y = \frac { 2 } { 5 } x - \frac { 32 } { 5 }$
B) $y = \frac { 3 } { 4 } x - \frac { 27 } { 4 }$
C) $y = - \frac { 2 } { 5 } x - \frac { 32 } { 5 }$
D) $y = - \frac { 3 } { 4 } x - \frac { 27 } { 4 }$

Accepted Answer

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

Question 3

Write the equation of the line with the given conditions.
-passing through $( - 8 , - 3 )$ and parallel to the line with equation $5 x - 7 y = 9$
A) $y = \frac { 7 } { 5 } x - \frac { 3 } { 5 }$
B) $y = - \frac { 5 } { 7 } x - \frac { 19 } { 7 }$
C) $y = - \frac { 8 } { 7 } x - \frac { 9 } { 7 }$
D) $y = \frac { 5 } { 7 } x + \frac { 19 } { 7 }$

Accepted Answer

The slope of the line $5x - 7y = 9$ is $\frac{5}{7}$. A line parallel to it will have the same slope. Using the point-slope form with point $(-8, -3)$, the equation is $y + 3 = \frac{5}{7}(x + 8)$, which simplifies to $y = \frac{5}{7}x + \frac{19}{7}$.

Question 4

(-5,2)  and  (-5,8) 
A)  y=2 
B)  x=-5 
C)  2 x+8 y=0 
D)  8 x+2 y=0

Accepted Answer

The x-coordinate for both points is -5, which means they lie on the vertical line x = -5.

Question 5

Write the equation of the line with the given conditions.
-passing through $( 3 , - 7 )$ and perpendicular to the line with equation $4 x - 5 y = - 23$
A) $y = - \frac { 5 } { 4 } x - \frac { 13 } { 4 }$
B) $y = - \frac { 4 } { 5 } x - \frac { 4 } { 5 }$
C) $y = \frac { 5 } { 4 } x - \frac { 13 } { 4 }$
D) $y = - \frac { 3 } { 5 } x - \frac { 23 } { 5 }$

Accepted Answer

The given line has a slope of 4/5. A line perpendicular to this line will have a slope of -5/4. The equation of a line with a slope of -5/4 and passing through the point (3, -7) is y = -5/4 x - 13/4.

Question 6

Write an equation of the line through the given point with the given slope. Write the equation in slope-intercept form.
-$$( 5,3 ) ; m = - \frac { 3 } { 8 }$$
A) $y = - \frac { 8 } { 3 } x - \frac { 8 } { 39 }$
B) $y = - \frac { 3 } { 8 } x + \frac { 8 } { 39 }$
C) $y = - \frac { 3 } { 8 } x + \frac { 39 } { 8 }$
D) $y = - \frac { 3 } { 8 } x - \frac { 39 } { 8 }$

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 $m = -\frac{3}{8}$ and a point $(5,3)$, we substitute $m$, $x$, and $y$ into the equation and solve for $b$: $3 = -\frac{3}{8}(5) + b$, leading to $b = \frac{39}{8}$. Thus, the equation is $y = -\frac{3}{8}x + \frac{39}{8}$.

Question 7

(8,-3)  and  (-8,-3) 
A)  x=8 
B)  -8 x+8 y=0 
C)  y=-3 
D)  8 x-8 y=0

Accepted Answer

The y-coordinate is the same for both points, indicating a horizontal line at y = -3.

Question 8

Write an equation of the line through the given point with the given slope. Write the equation in slope-intercept form.
-$$( 4 , - 3 ) ; m = - 9$$
A) $y = 9 x + 32$
B) $y = - 9 x + 31$
C) $y = - 9 x + 34$
D) $y = - 9 x + 33$

Accepted Answer

Using the point-slope form $y - y_1 = m(x - x_1)$ with point (4, -3) and slope -9, we get $y + 3 = -9(x - 4)$. Simplifying, $y = -9x + 36 - 3$, which gives $y = -9x + 33$.

Question 9

Write an equation of the line through the given point with the given slope. Write the equation in slope-intercept form.
-$( - 5,0 ) ; m = - 7$
A) $y = 7 x - 5$
B) $y = - 7 x - 35$
C) $y = 5 x - 7$
D) $y = - 5 x - 7$

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 point $(-5, 0)$ and slope $m = -7$, we substitute $x = -5$, $y = 0$, and $m = -7$ into the equation to find $b$. So, $0 = -7(-5) + b$, which simplifies to $0 = 35 + b$. Solving for $b$, we get $b = -35$. Therefore, the equation of the line is $y = -7x - 35$.

Question 10

Write the slope-intercept form of the equation for the line passing through the given pair of points.
-$( 9,5 )$ and $( 0 , - 3 )$
A) $y = \frac { 8 } { 9 } x - 3$
B) $y = \frac { 4 } { 3 } x - 3$
C) $y = - \frac { 8 } { 9 } x - 3$
D) $y = - \frac { 4 } { 3 } x - 3$

Accepted Answer

The slope $m$ of the line passing through points $(x_1, y_1)$ and $(x_2, y_2)$ is given by $m = \frac{y_2 - y_1}{x_2 - x_1}$. For the points $(9, 5)$ and $(0, -3)$, the slope is $m = \frac{-3 - 5}{0 - 9} = \frac{-8}{-9} = \frac{8}{9}$. Using the point-slope form and converting to slope-intercept form $y = mx + b$, where $m = \frac{8}{9}$ and using one of the points to solve for $b$, we get $y = \frac{8}{9}x - 3$.

Question 11

Write an equation of the line through the given point with the given slope. Write the equation in slope-intercept form.
-$( 4,3 ) ; m = - \frac { 2 } { 3 }$
A) $y = - \frac { 2 } { 3 } x + \frac { 3 } { 17 }$
B) $y = - \frac { 2 } { 3 } x + \frac { 17 } { 3 }$
C) $y = - \frac { 3 } { 2 } x + \frac { 17 } { 3 }$
D) $y = - \frac { 2 } { 3 } x - \frac { 17 } { 3 }$

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 $m = -\frac{2}{3}$ and a point $(4,3)$, we can substitute these values into the slope-intercept form to find $b$. Substituting $x = 4$ and $y = 3$ gives $3 = -\frac{2}{3}(4) + b$, solving for $b$ gives $b = \frac{17}{3}$. Therefore, the equation is $y = -\frac{2}{3}x + \frac{17}{3}$.

Question 12

(-4,6) ; m=-4 
A)  y=-4 x-11 
B)  y=-4 x-18 
C)  y=4 x-12 
D)  y=-4 x-10

Accepted Answer

The answer of  (-4,6) ; m=-4 
A)  y=-4...

Question 13

Write the slope-intercept form of the equation for the line passing through the given pair of points.
-$( - 7,1 )$ and $( 6,3 )$
A) $y = \frac { 2 } { 13 } x + \frac { 27 } { 13 }$
B) $y = - \frac { 8 } { 3 } x + 19$
C) $y = - \frac { 2 } { 13 } x + \frac { 27 } { 13 }$
D) $y = \frac { 8 } { 3 } x + 19$

Accepted Answer

The slope $m$ of the line passing through points $(-7, 1)$ and $(6, 3)$ is calculated as $m = \frac{3 - 1}{6 - (-7)} = \frac{2}{13}$. Using point-slope form and one of the points, for example, $(-7, 1)$, we can find the y-intercept $b$ by solving $1 = \frac{2}{13}(-7) + b$, which gives $b = \frac{27}{13}$. Thus, the equation in slope-intercept form is $y = \frac{2}{13}x + \frac{27}{13}$.

Question 14

Write the equation of the line with the given conditions.
-passing through $( 2,4 )$ and perpendicular to the line with equation $- 4 x + y = 3$
A) $y = - 4 x - 18$
B) $y = \frac { 1 } { 4 } x - \frac { 9 } { 2 }$
C) $y = - \frac { 1 } { 4 } x + \frac { 9 } { 2 }$
D) $y = - \frac { 1 } { 4 } x - \frac { 9 } { 2 }$

Accepted Answer

The slope of the given line is 4, so the slope of the perpendicular line is -1/4. The line passes through the point (2,4), so the equation of the line is y - 4 = (-1/4)(x - 2), which simplifies to y = -1/4x + 9/2.

Question 15

Write the equation of the line with the given conditions.
-passing through $( 5,2 )$ and parallel to the line with equation $2 x + y = 4$
A) $y = - 2 x + 12$
B) $y = - 2 x - 12$
C) $y = 2 x - 12$
D) $y = - \frac { 1 } { 2 } x - 6$

Accepted Answer

Lines that are parallel have the same slope. The given line $2x + y = 4$ can be rewritten in slope-intercept form as $y = -2x + 4$, indicating a slope of $-2$. A line parallel to this must also have a slope of $-2$. Using the point $(5,2)$ and the slope $-2$, we can find the equation of the line by using the point-slope form $y - y_1 = m(x - x_1)$, which gives $y - 2 = -2(x - 5)$. Simplifying this gives $y = -2x + 12$, which matches option A.

Question 16

Write the slope-intercept form of the equation for the line passing through the given pair of points.
-$( - 4,0 )$ and $( 5 , - 2 )$
A) $y = \frac { 4 } { 7 } x + \frac { 6 } { 7 }$
B) $y = - \frac { 2 } { 9 } x - \frac { 8 } { 9 }$
C) $y = \frac { 2 } { 9 } x - \frac { 8 } { 9 }$
D) $y = - \frac { 4 } { 7 } x + \frac { 6 } { 7 }$

Accepted Answer

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

Question 17

Write an equation of the line through the given point with the given slope. Write the equation in slope-intercept form.
-$( - 7,10 ) ; m = 0$
A) $y = \frac { 7 } { 10 } x + 0$
B) $y = \frac { 10 } { 7 } x + 0$
C) $y = 10$
D) $x = - 7$

Accepted Answer

The slope $m = 0$ indicates a horizontal line, which means the y-value remains constant for all x-values. Therefore, the equation is $y = 10$.

Question 18

(8,-2) ; m=-$\frac { 4 } { 5 }$
A)  y=  $\frac { 4 } { 5 } x - \frac { 22 } { 5 }$
B)  y=-$\frac { 4 } { 5 }$x+6 
C)  y=  $= \frac { 4 } { 5 } x + \frac { 42 } { 5 }$
D)  y=  $- \frac { 4 } { 5 } x + \frac { 22 } { 5 }$

Accepted Answer

To find the equation of the line with slope $m = -\frac{4}{5}$ passing through the point (8, -2), we use the point-slope form of a line equation: $y - y_1 = m(x - x_1)$, where $(x_1, y_1)$ is a point on the line. Substituting $m = -\frac{4}{5}$, $x_1 = 8$, and $y_1 = -2$, we get $y + 2 = -\frac{4}{5}(x - 8)$. Simplifying, $y = -\frac{4}{5}x + \frac{32}{5} - 2$, which simplifies further to $y = -\frac{4}{5}x + \frac{22}{5}$.

Question 19

(4,2)  and  (10,2) 
A)  10 x+4 y=0 
B)  x=4 
C)  4 x+10 y=0 
D)  y=2

Accepted Answer

The points (4,2) and (10,2) share the same y-coordinate, which means they lie on a horizontal line where y is constant. The equation representing this line is y=2.

Question 20

(-1,7) ;  horizontal
A)  y=7 
B)  x=-1 
C)  y=1 
D)  x=-7

Accepted Answer

A horizontal line means that the y-value remains constant across all points on the line. Since the given point is (-1,7), the y-value is 7, which corresponds to the equation y=7.

Quiz 1: Functions, Graphs, and Models; Linear Functions

y -intercept - 10 and x -intercept -9

Write the slope-intercept form of the equation for the line passing through the given pair of points. - $( - 5 , - 3 )$ and $( - 1 , - 6 )$

Write the equation of the line with the given conditions. -passing through $( - 8 , - 3 )$ and parallel to the line with equation $5 x - 7 y = 9$

(-5,2) and (-5,8)

Write the equation of the line with the given conditions. -passing through $( 3 , - 7 )$ and perpendicular to the line with equation $4 x - 5 y = - 23$

Write an equation of the line through the given point with the given slope. Write the equation in slope-intercept form. - $( 5,3 ) ; m = - \frac { 3 } { 8 }$

(8,-3) and (-8,-3)

Write an equation of the line through the given point with the given slope. Write the equation in slope-intercept form. - $( 4 , - 3 ) ; m = - 9$

Write an equation of the line through the given point with the given slope. Write the equation in slope-intercept form. - $( - 5,0 ) ; m = - 7$

Write the slope-intercept form of the equation for the line passing through the given pair of points. - $( 9,5 )$ and $( 0 , - 3 )$

Write an equation of the line through the given point with the given slope. Write the equation in slope-intercept form. - $( 4,3 ) ; m = - \frac { 2 } { 3 }$

(-4,6) ; m=-4

Write the slope-intercept form of the equation for the line passing through the given pair of points. - $( - 7,1 )$ and $( 6,3 )$

Write the equation of the line with the given conditions. -passing through $( 2,4 )$ and perpendicular to the line with equation $- 4 x + y = 3$

Write the equation of the line with the given conditions. -passing through $( 5,2 )$ and parallel to the line with equation $2 x + y = 4$

Write the slope-intercept form of the equation for the line passing through the given pair of points. - $( - 4,0 )$ and $( 5 , - 2 )$

Write an equation of the line through the given point with the given slope. Write the equation in slope-intercept form. - $( - 7,10 ) ; m = 0$

(8,-2) ; m=- $\frac { 4 } { 5 }$

(4,2) and (10,2)

(-1,7) ; horizontal

Quiz 1: Functions, Graphs, and Models; Linear Functions

y -intercept - 10 and x -intercept -9

Write the slope-intercept form of the equation for the line passing through the given pair of points. - (−5,−3) ( - 5 , - 3 ) (−5,−3) and (−1,−6) ( - 1 , - 6 ) (−1,−6)

Write the equation of the line with the given conditions. -passing through (−8,−3) ( - 8 , - 3 ) (−8,−3) and parallel to the line with equation 5x−7y=95 x - 7 y = 95x−7y=9

(-5,2) and (-5,8)

Write the equation of the line with the given conditions. -passing through (3,−7) ( 3 , - 7 ) (3,−7) and perpendicular to the line with equation 4x−5y=−234 x - 5 y = - 234x−5y=−23

Write an equation of the line through the given point with the given slope. Write the equation in slope-intercept form. - (5,3) ;m=−38( 5,3 ) ; m = - \frac { 3 } { 8 }(5,3) ;m=−83​

(8,-3) and (-8,-3)

Write an equation of the line through the given point with the given slope. Write the equation in slope-intercept form. - (4,−3) ;m=−9( 4 , - 3 ) ; m = - 9(4,−3) ;m=−9

Write an equation of the line through the given point with the given slope. Write the equation in slope-intercept form. - (−5,0) ;m=−7( - 5,0 ) ; m = - 7(−5,0) ;m=−7

Write the slope-intercept form of the equation for the line passing through the given pair of points. - (9,5) ( 9,5 ) (9,5) and (0,−3) ( 0 , - 3 ) (0,−3)

Write an equation of the line through the given point with the given slope. Write the equation in slope-intercept form. - (4,3) ;m=−23( 4,3 ) ; m = - \frac { 2 } { 3 }(4,3) ;m=−32​