Question 1

Graph the equation by determining the missing values needed to plot the ordered pairs.
-$$4 x - 5 y = - 20 ; ( 0 , \quad ) , ( , 0 ) , ( - 1 , \quad )$$

A)

B)

C)

D)

Accepted Answer

The answer of Graph the equation by determining the missing...

Question 2

Graph the equation by plotting points.
-$y=x^{2}-2$

A)

B)

C)

D)

Accepted Answer

The answer of Graph the equation by plotting points.
-$y=x^{2}-2$

A)

B)

C)

D)

...

Question 3

Graph the equation by determining the missing values needed to plot the ordered pairs.
-$$x + 3 y = 6 ; ( 0 , \quad ) , ( , 0 ) , ( 1 , \quad ) , ( , 1 )$$

A)

B)

C)

D)

Accepted Answer

The answer of Graph the equation by determining the missing...

Question 4

Find the coordinates of the other endpoint of the segment, given its midpoint and one endpoint.
-midpoint (b, x), endpoint (m, q) 
A) $( 2 b - m , 2 x - q )$
B) $\left( \frac { b + m } { 2 } , \frac { x + q } { 2 } \right)$
C) $( b - m , x - q )$
D) $( 2 m - b , 2 q - x )$

Accepted Answer

The midpoint formula is $\left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)$. Given the midpoint (b, x) and one endpoint (m, q), to find the other endpoint, you solve for $x_2$ and $y_2$, resulting in $x_2 = 2b - m$ and $y_2 = 2x - q$, which matches choice A.

Question 5

Graph the equation by determining the missing values needed to plot the ordered pairs.
-$$y - x = 1 ; ( 3 , \quad ) , ( \quad , 8 ) , ( 4 , \quad )$$

A)

B)

C)

D)

Accepted Answer

The answer of Graph the equation by determining the missing...

Question 6

Find the coordinates of the other endpoint of the segment, given its midpoint and one endpoint.
-midpoint (7, 13), endpoint (10, 9)
A) (18, 3)
B) (16, 1)
C) (4, 5)
D) (4, 17)

Accepted Answer

To find the other endpoint, use the midpoint formula: ((x1 + x2)/2, (y1 + y2)/2) = (7, 13). Solving for x2 and y2 gives x2 = 4 and y2 = 17.

Question 7

Determine whether the three points are collinear.
-(-5, -11), (4, 7), (5, 9)
A) Yes
B) No

Accepted Answer

The slope between (-5, -11) and (4, 7) is 3. The slope between (4, 7) and (5, 9) is 2. Since the slopes are not equal, the points are not collinear.

Question 8

Graph the equation by plotting points.
-$y=\sqrt{x+1}$

A)

B)

C)

D)

Accepted Answer

The answer of Graph the equation by plotting points.
-$y=\sqrt{x+1}$

A)

B)

C)

D)

...

Question 9

Determine whether the three points are collinear.
-(0, -12), (-1, -3), (-9, -11)
A) Yes
B) No

Accepted Answer

To determine if three points are collinear, we can use the slope formula, $m = \frac{y_2 - y_1}{x_2 - x_1}$, between each pair of points. If all slopes are equal, the points are collinear. For points (0, -12) and (-1, -3), the slope is $m_1 = \frac{-3 - (-12)}{-1 - 0} = \frac{9}{-1} = -9$. For points (-1, -3) and (-9, -11), the slope is $m_2 = \frac{-11 - (-3)}{-9 - (-1)} = \frac{-8}{-8} = 1$. Since $m_1 \neq m_2$, the points are not collinear.

Question 10

Determine whether the three points are collinear.
-(7, -3), (-3, 6), (1, 1)
A) Yes
B) No

Accepted Answer

To determine if three points are collinear, we can use the slope formula between each pair of points. If all slopes are equal, the points are collinear. The slope between the first two points (7, -3) and (-3, 6) is (6 - (-3)) / (-3 - 7) = 9 / -10. The slope between the first and third points (7, -3) and (1, 1) is (1 - (-3)) / (1 - 7) = 4 / -6 = 2 / -3. Since the slopes are not equal, the points are not collinear.

Question 11

Find the coordinates of the other endpoint of the segment, given its midpoint and one endpoint.
-The graph shows an idealized linear relationship for the average monthly payment to retirees from 1995 to 1999. Use the midpoint formula to estimate the average payment in 1997. Average Monthly Payment to Retirees

$$\begin{array} { c c c } 
1995 & 1997 & 1999 \
a = \$ 452 ; b = \$ 524 & &
\end{array}$$
A) $\$ 36$
B) $\$ 488$
C) $\$ 500$
D) $\$ 524$

Accepted Answer

The answer of Find the coordinates of the other endpoint...

Question 12

Find the coordinates of the other endpoint of the segment, given its midpoint and one endpoint.
-The table shows enrollment in 2-year technical schools for 1980, 1990 and 2000. Assuming a linear relationship, estimate the enrollment for 1995.
 $\begin{array}{c|c}
\text { Year } & \text { Enrollment (in millions) } \
\hline 1980 & 2.2 \
1990 & 2.7 \
2000 & 3.2
\end{array}$

A) $1.25$ million
B) $4.65$ million
C) $2.2$ million
D) $2.95$ million

Accepted Answer

The enrollment increases by 0.5 million every 10 years (from 2.2 million in 1980 to 2.7 million in 1990, and then to 3.2 million in 2000). Therefore, halfway through the decade (1995), the enrollment would be halfway between 2.7 million and 3.2 million, which is 2.95 million.

Question 13

Find the coordinates of the other endpoint of the segment, given its midpoint and one endpoint.
-midpoint $\left( \frac { \mathrm { p } + \mathrm { b } } { 2 } , \frac { \mathrm { q } - \mathrm { y } } { 2 } \right)$, endpoint $( \mathrm { p } , \mathrm { q } )$
A) $\left( \frac { 3 p + b } { 4 } , \frac { 3 q - y } { 4 } \right)$
B) $( b , y )$
C) $( b , - y )$
D) $\left( \frac { b } { 2 } , - \frac { y } { 2 } \right)$

Accepted Answer

The answer of Find the coordinates of the other endpoint...

Question 14

Graph the equation by determining the missing values needed to plot the ordered pairs.
-$$y + x = 4 ; ( 1 , \quad ) , ( 4 , \quad ) , ( 3 , \quad )$$

A)

B)

C)

D)

Accepted Answer

The answer of Graph the equation by determining the missing...

Question 15

Find the coordinates of the other endpoint of the segment, given its midpoint and one endpoint.
-The table lists how financial aid income cutoffs (in dollars) for a family of four have changed over time. Use the midpoint formula to approximate the financial aid cutoff for 1985.

$\begin{array}{c|c}
\text { Year } & \text { Income (in dollars) } \
\hline 1960 & 20,500 \
1970 & 26,000 \
1980 & 31,500 \
1990 & 37,000 \
2000 & 42,500
\end{array}$

A) $\$ 20,500$
B) $\$ 34,250$
C) $\$ 17,750$
D) $\$ 53,500$

Accepted Answer

To find the financial aid cutoff for 1985, we can use the midpoint formula between 1980 and 1990, since 1985 is the midpoint year between these two. The midpoint formula in this context is $\frac{31,500 + 37,000}{2} = 34,250$.

Question 16

Graph the equation by determining the missing values needed to plot the ordered pairs.
-$$4 y = - 2 x + 8 ; ( 0 , \quad ) , ( , 0 ) , ( 1 , \quad )$$

A)

B)

C)

D)

Accepted Answer

The answer of Graph the equation by determining the missing...

Question 17

Find the coordinates of the other endpoint of the segment, given its midpoint and one endpoint.
-midpoint (0, 3), endpoint (-4, 8)
A) (4, 13)
B) (4, -2)
C) (-14, 16)
D) (-12, 18)

Accepted Answer

To find the other endpoint, use the midpoint formula: ((x1 + x2)/2, (y1 + y2)/2) = (0, 3). Given one endpoint (-4, 8), solve for x2 and y2:  x2 = 2*0 - (-4) = 4  y2 = 2*3 - 8 = -2  Thus, the other endpoint is (4, -2).

Question 18

Find the coordinates of the other endpoint of the segment, given its midpoint and one endpoint.
-midpoint (5, 9), endpoint (2, 4)
A) (12, 10)
B) (8, -1)
C) (8, 14)
D) (-4, -6)

Accepted Answer

To find the other endpoint, use the midpoint formula: ((x1 + x2)/2, (y1 + y2)/2) = (5, 9). Solving for x2 and y2 gives x2 = 8 and y2 = 14.

Question 19

Find the coordinates of the other endpoint of the segment, given its midpoint and one endpoint.
-midpoint (0, -5), endpoint (2, -4)
A) (6, -2)
B) (0, -8)
C) (-2, -6)
D) (-2, -3)

Accepted Answer

The midpoint formula is $(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2})$. Given the midpoint (0, -5) and one endpoint (2, -4), we can solve for the other endpoint (x, y) by setting up equations: $0 = \frac{2 + x}{2}$ and $-5 = \frac{-4 + y}{2}$. Solving these gives x = -2 and y = -6, so the other endpoint is (-2, -6).

Question 20

Graph the equation by plotting points.
-$y=\sqrt{x}+3$

A)

B)
 
C)

D)

Accepted Answer

The answer of Graph the equation by plotting points.
-$y=\sqrt{x}+3$

A)

B)
 
C)

D)

...

Quiz 3: Graphs and Functions

Graph the equation by plotting points. - $y=x^{2}-2$ $Graph the equation by plotting points. - y=x^{2}-2 A) B) C) D)$

Find the coordinates of the other endpoint of the segment, given its midpoint and one endpoint. -midpoint (b, x) , endpoint (m, q)

Find the coordinates of the other endpoint of the segment, given its midpoint and one endpoint. -midpoint (7, 13) , endpoint (10, 9)

Determine whether the three points are collinear. -(-5, -11) , (4, 7) , (5, 9)

Graph the equation by plotting points. - $y=\sqrt{x+1}$ $Graph the equation by plotting points. - y=\sqrt{x+1} A) B) C) D)$

Determine whether the three points are collinear. -(0, -12) , (-1, -3) , (-9, -11)

Determine whether the three points are collinear. -(7, -3) , (-3, 6) , (1, 1)

Find the coordinates of the other endpoint of the segment, given its midpoint and one endpoint. -midpoint $\left( \frac { \mathrm { p } + \mathrm { b } } { 2 } , \frac { \mathrm { q } - \mathrm { y } } { 2 } \right)$ , endpoint $( \mathrm { p } , \mathrm { q } )$

Find the coordinates of the other endpoint of the segment, given its midpoint and one endpoint. -midpoint (0, 3) , endpoint (-4, 8)

Find the coordinates of the other endpoint of the segment, given its midpoint and one endpoint. -midpoint (5, 9) , endpoint (2, 4)

Find the coordinates of the other endpoint of the segment, given its midpoint and one endpoint. -midpoint (0, -5) , endpoint (2, -4)

Graph the equation by plotting points. - $y=\sqrt{x}+3$ $Graph the equation by plotting points. - y=\sqrt{x}+3 A) B) C) D)$

Quiz 3: Graphs and Functions

Graph the equation by determining the missing values needed to plot the ordered pairs. - 4x−5y=−20;(0,) ,(,0) ,(−1,) 4 x - 5 y = - 20 ; ( 0 , \quad ) , ( , 0 ) , ( - 1 , \quad ) 4x−5y=−20;(0,) ,(,0) ,(−1,)

Graph the equation by plotting points. - y=x2−2y=x^{2}-2y=x2−2

Graph the equation by determining the missing values needed to plot the ordered pairs. - x+3y=6;(0,) ,(,0) ,(1,) ,(,1) x + 3 y = 6 ; ( 0 , \quad ) , ( , 0 ) , ( 1 , \quad ) , ( , 1 ) x+3y=6;(0,) ,(,0) ,(1,) ,(,1)

Find the coordinates of the other endpoint of the segment, given its midpoint and one endpoint. -midpoint (b, x) , endpoint (m, q)

Graph the equation by determining the missing values needed to plot the ordered pairs. - y−x=1;(3,) ,(,8) ,(4,) y - x = 1 ; ( 3 , \quad ) , ( \quad , 8 ) , ( 4 , \quad ) y−x=1;(3,) ,(,8) ,(4,)

Find the coordinates of the other endpoint of the segment, given its midpoint and one endpoint. -midpoint (7, 13) , endpoint (10, 9)

Determine whether the three points are collinear. -(-5, -11) , (4, 7) , (5, 9)

Graph the equation by plotting points. - y=x+1y=\sqrt{x+1}y=x+1​

Determine whether the three points are collinear. -(0, -12) , (-1, -3) , (-9, -11)

Determine whether the three points are collinear. -(7, -3) , (-3, 6) , (1, 1)

Graph the equation by determining the missing values needed to plot the ordered pairs. - y+x=4;(1,) ,(4,) ,(3,) y + x = 4 ; ( 1 , \quad ) , ( 4 , \quad ) , ( 3 , \quad ) y+x=4;(1,) ,(4,) ,(3,)

Graph the equation by determining the missing values needed to plot the ordered pairs. - 4y=−2x+8;(0,) ,(,0) ,(1,) 4 y = - 2 x + 8 ; ( 0 , \quad ) , ( , 0 ) , ( 1 , \quad ) 4y=−2x+8;(0,) ,(,0) ,(1,)

Find the coordinates of the other endpoint of the segment, given its midpoint and one endpoint. -midpoint (0, 3) , endpoint (-4, 8)

Find the coordinates of the other endpoint of the segment, given its midpoint and one endpoint. -midpoint (5, 9) , endpoint (2, 4)

Find the coordinates of the other endpoint of the segment, given its midpoint and one endpoint. -midpoint (0, -5) , endpoint (2, -4)

Graph the equation by plotting points. - y=x+3y=\sqrt{x}+3y=x​+3

Graph the equation by plotting points. - $y=x^{2}-2$ $Graph the equation by plotting points. - y=x^{2}-2 A) B) C) D)$

Graph the equation by plotting points. - $y=\sqrt{x+1}$ $Graph the equation by plotting points. - y=\sqrt{x+1} A) B) C) D)$

Graph the equation by plotting points. - $y=\sqrt{x}+3$ $Graph the equation by plotting points. - y=\sqrt{x}+3 A) B) C) D)$