Question 1

Graph the equation. $y = \frac { 10 } { x ^ { 2 } }$
A) 
B) 
C) 
D)

Accepted Answer

The graph of a reciprocal function with a positive numerator and a positive denominator (as in this case) is a hyperbola. Specifically, this hyperbola will be centered at the origin and will open up and down along the y-axis and left and right along the x-axis. As x approaches 0, the function will increase without bound, meaning that the hyperbola will approach the x-axis but never touch it. As x moves further away from 0, the function will approach 0, meaning that the hyperbola will get closer and closer to the y-axis but never touch it. Therefore, the correct graph is option C.

Question 2

Find y if the line through (0, 2) and ( 2, y ) has a slope of $- \frac { 3 } { 2 }$
A) 5
B) -1
C) 10
D) 4

Accepted Answer

The slope of a line passing through two points (x1, y1) and (x2, y2) is given by (y2 - y1) / (x2 - x1). Using this formula, we can find the slope of the line passing through (0, 2) and (2, y) as (y - 2) / (2 - 0) = -3/2. Solving for y, we get y = 2 - (3/2) * 2 = 2 - 3 = -1.

Question 3

Graph the equation. y = $-$ x 3 $-$ 3
A) 
B) 
C) 
D)

Accepted Answer

D

Question 4

Find the distance between the points (3, -5) and (6, -1).
A) 2
B) 10
C) 8
D) 5

Accepted Answer

The distance between two points $(x_1, y_1)$ and $(x_2, y_2)$ in a plane is given by the formula $\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$. Applying this formula to the points (3, -5) and (6, -1), we get $\sqrt{(6-3)^2 + (-1+5)^2} = \sqrt{3^2 + 4^2} = \sqrt{9 + 16} = \sqrt{25} = 5$.

Question 5

Find the slope of the line determined by the points (3, 2) and (5, 6).
A) $- \frac { 1 } { 2 }$
B) $\frac { 1 } { 2 }$
C) $-$ 2
D) 2

Accepted Answer

The slope of a line passing through two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by:

$$	ext{slope} = \frac{y_2-y_1}{x_2-x_1}$$

In this case, we have $(x_1,y_1) = (3,2)$ and $(x_2,y_2) = (5,6)$, so:

$$	ext{slope} = \frac{6-2}{5-3} = \frac{4}{2} = 2$$

Therefore, the answer is choice D.

Question 6

Graph the equation. y = x + 4
A) 
B) 
C) 
D)

Accepted Answer

To graph this equation, we can begin by plotting the y-intercept, which is (0,4). From there, we can use the slope of 1 (which is the coefficient of x) to plot additional points. 
When x increases by 1, y increases by 1 as well (since the slope is 1). Thus, we can plot the point (1,5) which is one unit to the right and one unit up from the y-intercept. 
We can continue this pattern to plot more points and then connect them to form a straight line. The resulting line should pass through both the y-intercept and the point (1,5) and extend indefinitely in both directions. 
The graph that matches this description is choice B.

Question 7

The graph of an equation is symmetric with respect to the y axis if replacing x with $- x$ results in an equivalent equation.

Accepted Answer

This is the definition of symmetry with respect to the y axis. If switching x and -x results in an equivalent equation, then the graph will be symmetric with respect to the y axis.

Question 8

Graph the equation. y = $-$ 3 x $-$ 2
A) 
B) 
C) 
D)

Accepted Answer

The answer of Graph the equation. y = $-$ 3...

Question 9

Graph the equation. y = x 2 $-$ 2
A) 
B) 
C) 
D)

Accepted Answer

The answer of Graph the equation. y = x 2...

Question 10

The distance between $P _ { 1 }$ and $P _ { 2 }$ is the same as the distance between $P _ { 2 }$ and $P _ { 1 }$ .

Accepted Answer

This statement is expressing the concept of symmetry of distance. The distance between two points does not depend on the order in which they are named. Therefore, the distance between $P _ { 1 }$ and $P _ { 2 }$ is the same as the distance between $P _ { 2 }$ and $P _ { 1 }$.

Question 11

If the point $( 3 , - 5 )$ is on a graph that is symmetric with respect to the x axis, the point $( - 3 , - 5 )$ is also on the graph.

Accepted Answer

Symmetry with respect to the x-axis means that if a point $(a, b)$ is on the graph, then the point $(a, -b)$ is also on the graph. The given points do not reflect this relationship; they reflect symmetry with respect to the y-axis instead.

Question 12

For the point (1, 8) determine the point that is symmetric with respect to y -axis.
A) (1, -8)
B) (0, 8)
C) (-1, -8)
D) (-1, 8)

Accepted Answer

To find a point symmetric to (1, 8) with respect to the y-axis, you change the sign of the x-coordinate while keeping the y-coordinate the same. Thus, the symmetric point is (-1, 8).

Question 13

Determine the type of symmetry (symmetry with respect to the x axis, y axis, or origin) exhibited by the graph of the equation: x ² + 5 y = -6. A) symmetry with respect to the x axis B) symmetry with respect to the y axis C) symmetry with respect to the origin

Accepted Answer

If we replace x with -x, the equation becomes (-x)^2 + 5y = -6, which simplifies to x^2 + 5y = -6. Since this is not the same as the original equation, there is no symmetry with respect to the origin. However, if we replace y with -y, the equation becomes x^2 + 5(-y) = -6, which simplifies to x^2 - 5y = -6. This is the same as the original equation, so there is symmetry with respect to the y axis. There is no symmetry with respect to the x axis.

Question 14

Determine the type of symmetry (symmetry with respect to the x axis, y axis, or origin) exhibited by the graph of the equation: x 2 $-$ 4 x $-$ y 2 = 3.
A) symmetry with respect to the x axis
B) symmetry with respect to the origin
C) symmetry with respect to the y axis

Accepted Answer

The answer of Determine the type of symmetry (symmetry with...

Question 15

Find the distance between the points (14, 9) and (-1, -9).
A) $\sqrt { 183 }$
B) $3 \sqrt { 61 }$
C) $\sqrt { 61 }$
D) 61

Accepted Answer

The distance between two points (x1, y1) and (x2, y2) can be found using the distance formula:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Using this formula, we get:
d = sqrt((-1 - 14)^2 + (-9 - 9)^2)
d = sqrt((-15)^2 + (-18)^2)
d = sqrt(225 + 324)
d = sqrt(549)
d = sqrt(3^2 * 61)
d = 3sqrt(61)
Therefore, the distance between the given points is 3sqrt(61), which corresponds to answer choice B.

Question 16

Find x if the line through ( 2, 2) and ( x , 7) has a slope of $\frac { 9 } { 8 }$
A) -10
B) 3
C) 6
D) 11

Accepted Answer

The slope formula is: 
$$ m = \frac{y_2 - y_1}{x_2 - x_1} $$
We know that one point is (2,2) and the slope is $\frac{9}{8}$. We can use this information to solve for x.
$$\frac{9}{8} = \frac{7 - 2}{x - 2} $$
Multiplying both sides by $x-2$:
$$\frac{9}{8}(x-2) = 5$$
$$9x - 18 = 40$$
$$9x = 58$$
$$x = 6\frac{2}{3}$$
Therefore, the answer is C) 6.

Question 17

The slope of a line is the ratio of the horizontal change to the vertical change when moving from one point to another point.

Accepted Answer

The slope of a line is the ratio of the vertical change to the horizontal change when moving from one point to another point on the line.

Question 18

Find the slope of the line determined by the points ( $-$ 4, 0) and (0, $-$ 7).
A) $\frac { 7 } { 4 }$
B) $\frac { 4 } { 7 }$
C) $- \frac { 7 } { 4 }$
D) 0

Accepted Answer

Using the formula for slope, we have:

slope = $\frac{	ext{change in y}}{	ext{change in x}}$

slope = $\frac{-7-0}{0-(-4)}$

slope = $\frac{-7}{4}$

Therefore, the slope of the line is $\boxed{	extbf{(C)} -\frac { 7 } { 4 }}$.

Question 19

Find the slope of the line determined by the points (2, 1) and (7, -19).
A) $-$ 4
B) $\frac { 1 } { 4 }$
C) $- \frac { 1 } { 4 }$
D) 4

Accepted Answer

The slope of a line through points $(x_1, y_1)$ and $(x_2, y_2)$ is given by $m = \frac{y_2 - y_1}{x_2 - x_1}$. Substituting the given points, $m = \frac{-19 - 1}{7 - 2} = \frac{-20}{5} = -4$.

Question 20

Graph the equation. 3 x $-$ y = 2
A) 
B) 
C) 
D)

Accepted Answer

The answer of Graph the equation. 3 x $-$ y...

Quiz 12: Coordinate Geometry: Lines, Parabolas, Circles, Ellipses and Hyperbolas

Graph the equation. $y = \frac { 10 } { x ^ { 2 } }$

Find y if the line through (0, 2) and ( 2, y ) has a slope of $- \frac { 3 } { 2 }$

Graph the equation. y = $-$ x 3 $-$ 3

Find the distance between the points (3, -5) and (6, -1) .

Find the slope of the line determined by the points (3, 2) and (5, 6) .

Graph the equation. y = x + 4

The graph of an equation is symmetric with respect to the y axis if replacing x with $- x$ results in an equivalent equation.

Graph the equation. y = $-$ 3 x $-$ 2

Graph the equation. y = x 2 $-$ 2

The distance between $P _ { 1 }$ and $P _ { 2 }$ is the same as the distance between $P _ { 2 }$ and $P _ { 1 }$ .

If the point $( 3 , - 5 )$ is on a graph that is symmetric with respect to the x axis, the point $( - 3 , - 5 )$ is also on the graph.

For the point (1, 8) determine the point that is symmetric with respect to y -axis.

Determine the type of symmetry (symmetry with respect to the x axis, y axis, or origin) exhibited by the graph of the equation: x ² + 5 y = -6.

Determine the type of symmetry (symmetry with respect to the x axis, y axis, or origin) exhibited by the graph of the equation: x 2 $-$ 4 x $-$ y 2 = 3.

Find the distance between the points (14, 9) and (-1, -9) .

Find x if the line through ( 2, 2) and ( x , 7) has a slope of $\frac { 9 } { 8 }$

The slope of a line is the ratio of the horizontal change to the vertical change when moving from one point to another point.

Find the slope of the line determined by the points ( $-$ 4, 0) and (0, $-$ 7) .

Find the slope of the line determined by the points (2, 1) and (7, -19) .

Graph the equation. 3 x $-$ y = 2

Quiz 12: Coordinate Geometry: Lines, Parabolas, Circles, Ellipses and Hyperbolas

Graph the equation. y=10x2y = \frac { 10 } { x ^ { 2 } }y=x210​

Find y if the line through (0, 2) and ( 2, y ) has a slope of −32- \frac { 3 } { 2 }−23​

Graph the equation. y = −-− x 3 −-− 3

Find the distance between the points (3, -5) and (6, -1) .

Find the slope of the line determined by the points (3, 2) and (5, 6) .

Graph the equation. y = x + 4

The graph of an equation is symmetric with respect to the y axis if replacing x with −x- x−x results in an equivalent equation.

Graph the equation. y = −-− 3 x −-− 2

Graph the equation. y = x 2 −-− 2

The distance between P1P _ { 1 }P1​ and P2P _ { 2 }P2​ is the same as the distance between P2P _ { 2 }P2​ and P1P _ { 1 }P1​ .

If the point (3,−5)( 3 , - 5 )(3,−5) is on a graph that is symmetric with respect to the x axis, the point (−3,−5)( - 3 , - 5 )(−3,−5) is also on the graph.

For the point (1, 8) determine the point that is symmetric with respect to y -axis.

Determine the type of symmetry (symmetry with respect to the x axis, y axis, or origin) exhibited by the graph of the equation: x 2 + 5 y = -6.

Determine the type of symmetry (symmetry with respect to the x axis, y axis, or origin) exhibited by the graph of the equation: x 2 −-− 4 x −-− y 2 = 3.

Find the distance between the points (14, 9) and (-1, -9) .

Find x if the line through ( 2, 2) and ( x , 7) has a slope of 98\frac { 9 } { 8 }89​

The slope of a line is the ratio of the horizontal change to the vertical change when moving from one point to another point.

Find the slope of the line determined by the points ( −-− 4, 0) and (0, −-− 7) .

Find the slope of the line determined by the points (2, 1) and (7, -19) .

Graph the equation. 3 x −-− y = 2

Graph the equation. $y = \frac { 10 } { x ^ { 2 } }$

Find y if the line through (0, 2) and ( 2, y ) has a slope of $- \frac { 3 } { 2 }$

Graph the equation. y = $-$ x 3 $-$ 3

The graph of an equation is symmetric with respect to the y axis if replacing x with $- x$ results in an equivalent equation.

Graph the equation. y = $-$ 3 x $-$ 2

Graph the equation. y = x 2 $-$ 2

The distance between $P _ { 1 }$ and $P _ { 2 }$ is the same as the distance between $P _ { 2 }$ and $P _ { 1 }$ .

If the point $( 3 , - 5 )$ is on a graph that is symmetric with respect to the x axis, the point $( - 3 , - 5 )$ is also on the graph.

Determine the type of symmetry (symmetry with respect to the x axis, y axis, or origin) exhibited by the graph of the equation: x ² + 5 y = -6.

Determine the type of symmetry (symmetry with respect to the x axis, y axis, or origin) exhibited by the graph of the equation: x 2 $-$ 4 x $-$ y 2 = 3.

Find x if the line through ( 2, 2) and ( x , 7) has a slope of $\frac { 9 } { 8 }$

Find the slope of the line determined by the points ( $-$ 4, 0) and (0, $-$ 7) .

Graph the equation. 3 x $-$ y = 2