Question 1

Determine whether the indicated ordered pair lies on the graph of the given equation.
-$$y = 8 x ^ { 2 } - 1 , ( - 1,7 )$$
A)Yes
B)No

Accepted Answer

To determine if the ordered pair $(-1, 7)$ lies on the graph of the equation $y = 8x^2 - 1$, substitute $x = -1$ into the equation and see if $y$ equals 7. Substituting, we get $y = 8(-1)^2 - 1 = 8(1) - 1 = 7$. Since this matches the $y$-value of the ordered pair, $(-1, 7)$ does lie on the graph of the equation.

Question 2

Plot the ordered pair in the Cartesian plane, and state in which quadrant or on which axis it lies.
-(1, -5)  
A) Quadrant I

B) Quadrant II

C) Quadrant III

D) Quadrant IV

Accepted Answer

D

Question 3

Plot the ordered pair in the Cartesian plane, and state in which quadrant or on which axis it lies.
-(-1, -5) 
A) Quadrant III

B) Quadrant IV

C) Quadrant II

D) Quadrant III

Accepted Answer

D

Question 4

Find the midpoint of the line segment joining the points A and B.
-A = (3, 5); B = (9, 3) 
A) $( 4,6 )$
B) $( 6,4 )$
C) $( 12,8 )$
D) $( - 6,2 )$

Accepted Answer

The midpoint of a line segment with endpoints $(x_1, y_1)$ and $(x_2, y_2)$ is given by $\left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)$. For points A = (3, 5) and B = (9, 3), the midpoint is $\left( \frac{3 + 9}{2}, \frac{5 + 3}{2} \right) = (6, 4)$.

Question 5

Determine whether the indicated ordered pair lies on the graph of the given equation.
-y = |x|, (3, -3)
A)Yes
B)No

Accepted Answer

The absolute value function |x| always produces non-negative outputs for any real number input x. Since (3, -3) has a negative y-value, it does not lie on the graph of y = |x|.

Question 6

Find the midpoint of the line segment joining the points A and B.
-A = (7, 1); B = (-16, -16) 
A) $( - 9 , - 15 )$
B) $\left( \frac { 23 } { 2 } , \frac { 17 } { 2 } \right)$
C) $\left( - \frac { 9 } { 2 } , - \frac { 15 } { 2 } \right)$
D) $( 9,15 )$

Accepted Answer

The midpoint formula is $\left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)$. Applying this to points A(7, 1) and B(-16, -16) gives $\left( \frac{7 - 16}{2}, \frac{1 - 16}{2} \right) = \left( -\frac{9}{2}, -\frac{15}{2} \right)$.

Question 7

Determine whether the indicated ordered pair lies on the graph of the given equation.
-$$y = 9 x ^ { 2 } + 1 , ( - 1 , - 8 )$$
A)Yes
B)No

Accepted Answer

Substituting $x = -1$ into the equation $y = 9x^2 + 1$, we get $y = 9(-1)^2 + 1 = 9 + 1 = 10$, not $-8$. Therefore, the point $(-1, -8)$ does not lie on the graph.

Question 8

Plot the ordered pair in the Cartesian plane, and state in which quadrant or on which axis it lies.
-(-4, 6)

A) Quadrant II

B) Quadrant I

C) Quadrant III

D) Quadrant IV

Accepted Answer

The answer of Plot the ordered pair in the Cartesian...

Question 9

Sketch the graph for the equation by plotting points.
-x2 + 9y = 9 
A)

B)

C)

D)

Accepted Answer

The answer of Sketch the graph for the equation by...

Question 10

Determine whether the indicated ordered pair lies on the graph of the given equation.
-$$y = \sqrt { x } - 4 , ( 9 , - 1 )$$
A)Yes
B)No

Accepted Answer

To determine if the ordered pair $(9, -1)$ lies on the graph of the equation $y = \sqrt{x} - 4$, substitute $x = 9$ into the equation and see if $y$ equals $-1$. Substituting $x = 9$ gives $y = \sqrt{9} - 4 = 3 - 4 = -1$, which matches the $y$-value of the ordered pair. Therefore, the ordered pair $(9, -1)$ does lie on the graph of the given equation.

Question 11

Plot the ordered pair in the Cartesian plane, and state in which quadrant or on which axis it lies.
-(6, 0) 
A) Quadrant II

B) $y$-axis

C) $x$-axis

D) $x$-axis

Accepted Answer

The answer of Plot the ordered pair in the Cartesian...

Question 12

Determine whether the indicated ordered pair lies on the graph of the given equation.
-$$y = | x | , ( - 3,3 )$$
A)Yes
B)No

Accepted Answer

The absolute value of -3 is 3, so when x = -3, y = 3, which matches the given ordered pair.

Question 13

Plot the ordered pair in the Cartesian plane, and state in which quadrant or on which axis it lies.
-(0, 4) 
A) $x$-axis

B) Quadrant II

C) $y$-axis

D) $y$-axis

Accepted Answer

The answer of Plot the ordered pair in the Cartesian...

Question 14

Sketch the graph for the equation by plotting points.
-4x + 2y = 8 
A)

B)

C)

D)

Accepted Answer

The answer of Sketch the graph for the equation by...

Question 15

Find the midpoint of the line segment joining the points A and B.
-A = (y, 2); B = (0, 8) 
A) $\left( \frac { y } { 2 } , 5 \right)$
B) $( y , 5 )$
C) $( \mathrm { y } , 10 )$
D) $\left( - \frac { y } { 2 } , 6 \right)$

Accepted Answer

The midpoint of a line segment with endpoints $(x_1, y_1)$ and $(x_2, y_2)$ is given by $\left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)$. For points A = (y, 2) and B = (0, 8), the midpoint is $\left( \frac{y + 0}{2}, \frac{2 + 8}{2} \right) = \left( \frac{y}{2}, 5 \right)$.

Question 16

Sketch the graph for the equation by plotting points.
-y = x + 3 
A)

B)

C)

D)

Accepted Answer

The answer of Sketch the graph for the equation by...

Question 17

Find the midpoint of the line segment joining the points A and B.
-A = (5, -9); B = (-2, -3) 
A) $\left( \frac { 3 } { 2 } , - 6 \right)$
B) $\left( \frac { 7 } { 2 } , - 3 \right)$
C) $( 3 , - 12 )$
D) $( 7 , - 6 )$

Accepted Answer

The midpoint of a line segment with endpoints $(x_1, y_1)$ and $(x_2, y_2)$ is given by $\left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right)$. For points A = (5, -9) and B = (-2, -3), the midpoint is $\left( \frac{5 + (-2)}{2}, \frac{-9 + (-3)}{2} \right) = \left( \frac{3}{2}, -6 \right)$.

Question 18

Sketch the graph for the equation by plotting points.
-y = 2x - 6 
A)

B)

C)

D)

Accepted Answer

The answer of Sketch the graph for the equation by...

Question 19

Plot the ordered pair in the Cartesian plane, and state in which quadrant or on which axis it lies.
-(2, 3) 
A) Quadrant II

B) Quadrant IV

C) Quadrant I

D) Quadrant I

Accepted Answer

The answer of Plot the ordered pair in the Cartesian...

Question 20

Determine whether the indicated ordered pair lies on the graph of the given equation.
-$$y = \sqrt { x } - 4 , ( 4,0 )$$
A)Yes
B)No

Accepted Answer

The answer of Determine whether the indicated ordered pair lies...

Quiz 2: The Rectangular Coordinate System, Lines, and Circles

Determine whether the indicated ordered pair lies on the graph of the given equation. - $y = 8 x ^ { 2 } - 1 , ( - 1,7 )$

Plot the ordered pair in the Cartesian plane, and state in which quadrant or on which axis it lies. -(1, -5)

Plot the ordered pair in the Cartesian plane, and state in which quadrant or on which axis it lies. -(-1, -5)

Find the midpoint of the line segment joining the points A and B. -A = (3, 5) ; B = (9, 3)

Determine whether the indicated ordered pair lies on the graph of the given equation. -y = |x|, (3, -3)

Find the midpoint of the line segment joining the points A and B. -A = (7, 1) ; B = (-16, -16)

Determine whether the indicated ordered pair lies on the graph of the given equation. - $y = 9 x ^ { 2 } + 1 , ( - 1 , - 8 )$

Plot the ordered pair in the Cartesian plane, and state in which quadrant or on which axis it lies. -(-4, 6)

Sketch the graph for the equation by plotting points. -x2 + 9y = 9

Determine whether the indicated ordered pair lies on the graph of the given equation. - $y = \sqrt { x } - 4 , ( 9 , - 1 )$

Plot the ordered pair in the Cartesian plane, and state in which quadrant or on which axis it lies. -(6, 0)

Determine whether the indicated ordered pair lies on the graph of the given equation. - $y = | x | , ( - 3,3 )$

Plot the ordered pair in the Cartesian plane, and state in which quadrant or on which axis it lies. -(0, 4)

Sketch the graph for the equation by plotting points. -4x + 2y = 8

Find the midpoint of the line segment joining the points A and B. -A = (y, 2) ; B = (0, 8)

Sketch the graph for the equation by plotting points. -y = x + 3

Find the midpoint of the line segment joining the points A and B. -A = (5, -9) ; B = (-2, -3)

Sketch the graph for the equation by plotting points. -y = 2x - 6

Plot the ordered pair in the Cartesian plane, and state in which quadrant or on which axis it lies. -(2, 3)

Determine whether the indicated ordered pair lies on the graph of the given equation. - $y = \sqrt { x } - 4 , ( 4,0 )$

Quiz 2: The Rectangular Coordinate System, Lines, and Circles

Determine whether the indicated ordered pair lies on the graph of the given equation. - y=8x2−1,(−1,7) y = 8 x ^ { 2 } - 1 , ( - 1,7 ) y=8x2−1,(−1,7)

Plot the ordered pair in the Cartesian plane, and state in which quadrant or on which axis it lies. -(1, -5)

Plot the ordered pair in the Cartesian plane, and state in which quadrant or on which axis it lies. -(-1, -5)

Find the midpoint of the line segment joining the points A and B. -A = (3, 5) ; B = (9, 3)

Determine whether the indicated ordered pair lies on the graph of the given equation. -y = |x|, (3, -3)

Find the midpoint of the line segment joining the points A and B. -A = (7, 1) ; B = (-16, -16)

Determine whether the indicated ordered pair lies on the graph of the given equation. - y=9x2+1,(−1,−8) y = 9 x ^ { 2 } + 1 , ( - 1 , - 8 ) y=9x2+1,(−1,−8)

Plot the ordered pair in the Cartesian plane, and state in which quadrant or on which axis it lies. -(-4, 6)

Sketch the graph for the equation by plotting points. -x2 + 9y = 9

Determine whether the indicated ordered pair lies on the graph of the given equation. - y=x−4,(9,−1) y = \sqrt { x } - 4 , ( 9 , - 1 ) y=x​−4,(9,−1)

Plot the ordered pair in the Cartesian plane, and state in which quadrant or on which axis it lies. -(6, 0)

Determine whether the indicated ordered pair lies on the graph of the given equation. - y=∣x∣,(−3,3) y = | x | , ( - 3,3 ) y=∣x∣,(−3,3)

Plot the ordered pair in the Cartesian plane, and state in which quadrant or on which axis it lies. -(0, 4)

Sketch the graph for the equation by plotting points. -4x + 2y = 8

Find the midpoint of the line segment joining the points A and B. -A = (y, 2) ; B = (0, 8)

Sketch the graph for the equation by plotting points. -y = x + 3

Find the midpoint of the line segment joining the points A and B. -A = (5, -9) ; B = (-2, -3)

Sketch the graph for the equation by plotting points. -y = 2x - 6

Plot the ordered pair in the Cartesian plane, and state in which quadrant or on which axis it lies. -(2, 3)

Determine whether the indicated ordered pair lies on the graph of the given equation. - y=x−4,(4,0) y = \sqrt { x } - 4 , ( 4,0 ) y=x​−4,(4,0)

Determine whether the indicated ordered pair lies on the graph of the given equation. - $y = 8 x ^ { 2 } - 1 , ( - 1,7 )$

Determine whether the indicated ordered pair lies on the graph of the given equation. - $y = 9 x ^ { 2 } + 1 , ( - 1 , - 8 )$

Determine whether the indicated ordered pair lies on the graph of the given equation. - $y = \sqrt { x } - 4 , ( 9 , - 1 )$

Determine whether the indicated ordered pair lies on the graph of the given equation. - $y = | x | , ( - 3,3 )$

Determine whether the indicated ordered pair lies on the graph of the given equation. - $y = \sqrt { x } - 4 , ( 4,0 )$