Question 1

Find the slope of the line through $P ( - 8,8 )$ and $Q ( 1 , - 37 )$.
A) $\quad m = - 4$
B) $\quad m = - 7$
C) $\quad m = - 3$
D) $m = - 5$
E) $\quad m = - 6$

Accepted Answer

The slope $m$ of a line through two 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 $P(-8, 8)$ and $Q(1, -37)$ into the formula gives $m = \frac{-37 - 8}{1 - (-8)} = \frac{-45}{9} = -5$.

Question 2

Find the midpoint of the line segment $P Q$.
$$P ( 10,3 ) , Q ( 4,9 )$$
A) $\quad M ( 9,6 )$
B) $\quad M ( 12,9 )$
C) $M ( 7,5 )$
D) $\quad M ( 1,0 )$
E) $M ( 7,6 )$

Accepted Answer

E

Question 3

Draw the line using the slope and $y$-intercept.
$$y + 1 = 2 x$$
A)

B)

C)

D)

Accepted Answer

D

Question 4

Determine whether the line through the points $P ( 8,34 ) , Q ( 12,16 )$ and the line through $R ( 4,17 ) , S ( 6,8 )$ are parallel, perpendicular, or neither.
A) neither
B) parallel
C) perpendicular

Accepted Answer

First, we need to find the slopes of the two lines:
- The slope of line PQ is (16-34)/(12-8) = -18/4 = -9/2.
- The slope of line RS is (8-17)/(6-4) = -9/2.
Since the slopes are the same, the lines are parallel. Therefore, the answer is B.

Question 5

Graph the equation.
$$y = 3 | x |$$
A)

B)

C)

D)

Accepted Answer

The answer of Graph the equation.
\[y = 3 | x...

Question 6

Find the slope of the line. $11 x - 3 = 10 ( y + x )$
A) $\quad m = \frac { 1 } { 10 }$
B) $\quad m = \frac { 3 } { 11 }$
C) $m = 10$
D) $m = - \frac { 1 } { 10 }$
E) $m = 11$
F) $m = \frac { 11 } { 10 }$

Accepted Answer

First, we need to put the equation in slope-intercept form, which means solving for y. To do this, we start by distributing the 10 on the right side:

$11x - 3 = 10y + 10x$

Subtracting 10x from both sides:

$x - 3 = 10y$

Dividing both sides by 10:

$\frac{1}{10} x - \frac{3}{10} = y$

This is now in the form $y = mx + b$ where $m$ is the slope. Therefore, the slope of the line is $\frac{1}{10}$. So the answer is A.

Question 7

Find the equation of the line parallel to the line $x = 3$ and passing through the midpoint of the segment joining $( 9,3 )$ and $( 5 , - 1 )$.
A) $\quad x = 1$
B) $\quad x = 9$
C) $\quad x = 7$
D) $\quad y = - 5$
E) $\quad x = 4$

Accepted Answer

The answer of Find the equation of the line parallel...

Question 8

Find the graph of the equation. $3 x - y = 2$

A)

B)

C)

D)

E)

Accepted Answer

The answer of Find the graph of the equation. \(3...

Question 9

In the following exercise, assume straight-line depreciation. A word processor costs $570.00 when new and is expected to be worth $195.00 after 5 years.What will It be worth after 2 years? 
A) $ \$ 570.00$
B) $\$ 382.50$
C) $\$ 420.00$
D) $\$195.00$
E) $\$375.00$

Accepted Answer

The depreciation per year is $(570 - 195) / 5 = 75$. After 2 years, the value is $570 - 2*75 = 420$.

Question 10

Find the slope of the line. $$2 ( x - 16 ) = 25 y + 21$$
A) $m = 25$
B) $m = \frac { 16 } { 25 }$
C) $m = \frac { 4 } { 25 }$
D) $\quad m = \frac { 2 } { 25 }$
E) $m = - \frac { 2 } { 25 }$
F) $m = 2$

Accepted Answer

We need to put the equation in slope-intercept form, which is in the form of $y=mx+b$. First, we simplify the given equation: $$2 ( x - 16 ) = 25 y + 21$$
$$2x-32 = 25y +21$$
$$25y=2x-53$$
$$y=\frac{2}{25}x-\frac{53}{25}$$
The slope of the line is the coefficient of $x$ in this equation, which is $\boxed{\frac{2}{25}}$.

Question 11

Write the equation of the line that passes through the point $P ( 0,0 )$ and is parallel to the line $y = 10 x - 9$.
A) $\quad y = - 9 x$
B) $\quad y = 10 x$
C) $\quad x = 10 y$
D) $\quad y = 9 x + 10$
E) $\quad y = 9 x$

Accepted Answer

Parallel lines have the same slope. The given line has a slope of 10, so the line parallel to it and passing through (0,0) is $y = 10x$.

Question 12

Find the x-intercept of the function. $$5 x + 13 y = 15$$
A) $\quad ( 0,15 / 13 )$
B) $( 1 / 3,0 )$
C) $( 3,0 )$
D) $( 0,3 )$
E) $\quad ( 15 / 13,0 )$

Accepted Answer

To find the x-intercept, set $y = 0$ and solve for $x$. Substituting $y = 0$ into the equation $5x + 13y = 15$ gives $5x = 15$, which simplifies to $x = 3$.

Question 13

Graph the equation. $y = 4 - | x |$
A)

B)

C)

D)

Accepted Answer

The answer of Graph the equation. \(y = 4 -...

Question 14

Use the slope-intercept form to write the equation of the line passing through the point $P ( 24,2 )$ and having the slope $m = - \frac { 1 } { 2 }$. Express the answer in general form.
A) $\quad y = \frac { 1 } { 2 } x + 1$
B) $\quad x + 2 y = - 28$
C) $\quad x + 2 y = 28$
D) $\quad x - 2 y = - 12$
E) $x - 2 y = 28$

Accepted Answer

The answer of Use the slope-intercept form to write the...

Question 15

Find the slope of the line. $$y = 17 x + 29$$
A) $\quad m = 17$
B) $\quad m = 18$
C) $\quad m = 14$
D) $\quad m = 21$
E) $\quad m = - 17$

Accepted Answer

In the equation $y = 17x + 29$, the coefficient of $x$ (the term with $x$) is $17$. This is also known as the slope of the line. Therefore, $m = 17$. The correct choice is $\boxed{	ext{(A)}}$.

Question 16

Graph the equation. $$y = x ^ { 2 } + 2 x$$
A)

B)

C)

D)

Accepted Answer

The graph is a parabola with a minimum point, and opens upward, indicating a positive leading coefficient. This can be determined by the equation being in the form of $y = ax^2 + bx + c$, where $a > 0$, $b = 2$, and $c = 0$. The vertex can be found by completing the square or using the formula $(-b/2a, f(-b/2a))$. The vertex is $(-1, -1)$, and the y-intercept is $y = 0$. Therefore, the best choice is B.

Question 17

Use point-slope form to write the equation of the line. 
A) $\quad y = 4 x + 6$
B) $\quad y = 4 x + 7$
C) $y = 4 x - 6$
D) $\quad y = 6 x + 4$
E) none of these

Accepted Answer

The answer of Use point-slope form to write the equation...

Question 18

Indicate the quadrant in which the point (- 9, - 2) lies. 
A) quadrant II
B) quadrant I
C) quadrant III
D) quadrant IV
E) none of these

Accepted Answer

The point (-9, -2) is in the third quadrant because both x and y coordinates are negative.

Question 19

Write the equation of the line that passes through the point $P ( 0,0 )$ and is perpendicular to the line $y = -$ $4 x + 10$.
A) $\quad y = 4 x$
B) $y = - \frac { 1 } { 4 } x + 10$
C) $y = \frac { 1 } { 4 } x$
D) $\quad y = - 10 x$
E) $y = - \frac { 1 } { 10 } x$

Accepted Answer

The slope of the given line is $-4$, so the slope of the line perpendicular to it is $\frac{-1}{-4}=\frac{1}{4}$. We also know that the line passes through point $(0,0)$, so using the point-slope formula we get $$y-0=\frac{1}{4}(x-0) \Rightarrow y=\frac{1}{4}x$$ Thus the equation of the line that passes through point $P(0,0)$ and is perpendicular to the given line is $\boxed{	extbf{(C) } y=\frac{1}{4}x}$.

Question 20

True or False? The points $A , B , C$ and $D$ are vertices of a square.
$$A ( 4,2 ) ; B ( 6,3 ) ; C ( 5,5 ) ; D ( 3,4 )$$

Accepted Answer

The distance between points AB and BC is not equal to the distance between points CD and DA, so the figure cannot be a square.

Quiz 3: The Rectangular Coordinate System and Graphs of Equations

Find the slope of the line through $P ( - 8,8 )$ and $Q ( 1 , - 37 )$ .

Find the midpoint of the line segment $P Q$ . $P ( 10,3 ) , Q ( 4,9 )$

Draw the line using the slope and $y$ -intercept. $y + 1 = 2 x$

Determine whether the line through the points $P ( 8,34 ) , Q ( 12,16 )$ and the line through $R ( 4,17 ) , S ( 6,8 )$ are parallel, perpendicular, or neither.

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

Find the slope of the line. $11 x - 3 = 10 ( y + x )$

Find the equation of the line parallel to the line $x = 3$ and passing through the midpoint of the segment joining $( 9,3 )$ and $( 5 , - 1 )$ .

Find the graph of the equation. $3 x - y = 2$

In the following exercise, assume straight-line depreciation. A word processor costs $570.00 when new and is expected to be worth $195.00 after 5 years.What will It be worth after 2 years?

Find the slope of the line. $2 ( x - 16 ) = 25 y + 21$

Write the equation of the line that passes through the point $P ( 0,0 )$ and is parallel to the line $y = 10 x - 9$ .

Find the x-intercept of the function. $5 x + 13 y = 15$

Graph the equation. $y = 4 - | x |$

Use the slope-intercept form to write the equation of the line passing through the point $P ( 24,2 )$ and having the slope $m = - \frac { 1 } { 2 }$ . Express the answer in general form.

Find the slope of the line. $y = 17 x + 29$

Graph the equation. $y = x ^ { 2 } + 2 x$

Use point-slope form to write the equation of the line. $Use point-slope form to write the equation of the line. A) \quad y = 4 x + 6 B) \quad y = 4 x + 7 C) y = 4 x - 6 D) \quad y = 6 x + 4 E) none of these$

Indicate the quadrant in which the point (- 9, - 2) lies.

Write the equation of the line that passes through the point $P ( 0,0 )$ and is perpendicular to the line $y = -$ $4 x + 10$ .

True or False? The points $A , B , C$ and $D$ are vertices of a square. $A ( 4,2 ) ; B ( 6,3 ) ; C ( 5,5 ) ; D ( 3,4 )$

Quiz 3: The Rectangular Coordinate System and Graphs of Equations

Find the slope of the line through P(−8,8) P ( - 8,8 ) P(−8,8) and Q(1,−37) Q ( 1 , - 37 ) Q(1,−37) .

Find the midpoint of the line segment PQP QPQ . P(10,3) ,Q(4,9) P ( 10,3 ) , Q ( 4,9 ) P(10,3) ,Q(4,9)

Draw the line using the slope and yyy -intercept. y+1=2xy + 1 = 2 xy+1=2x

Determine whether the line through the points P(8,34) ,Q(12,16) P ( 8,34 ) , Q ( 12,16 ) P(8,34) ,Q(12,16) and the line through R(4,17) ,S(6,8) R ( 4,17 ) , S ( 6,8 ) R(4,17) ,S(6,8) are parallel, perpendicular, or neither.

Graph the equation. y=3∣x∣y = 3 | x |y=3∣x∣

Find the slope of the line. 11x−3=10(y+x) 11 x - 3 = 10 ( y + x ) 11x−3=10(y+x)

Find the equation of the line parallel to the line x=3x = 3x=3 and passing through the midpoint of the segment joining (9,3) ( 9,3 ) (9,3) and (5,−1) ( 5 , - 1 ) (5,−1) .

Find the graph of the equation. 3x−y=23 x - y = 23x−y=2

In the following exercise, assume straight-line depreciation. A word processor costs $570.00 when new and is expected to be worth $195.00 after 5 years.What will It be worth after 2 years?

Find the slope of the line. 2(x−16) =25y+212 ( x - 16 ) = 25 y + 212(x−16) =25y+21

Write the equation of the line that passes through the point P(0,0) P ( 0,0 ) P(0,0) and is parallel to the line y=10x−9y = 10 x - 9y=10x−9 .

Find the x-intercept of the function. 5x+13y=155 x + 13 y = 155x+13y=15

Graph the equation. y=4−∣x∣y = 4 - | x |y=4−∣x∣

Use the slope-intercept form to write the equation of the line passing through the point P(24,2) P ( 24,2 ) P(24,2) and having the slope m=−12m = - \frac { 1 } { 2 }m=−21​ . Express the answer in general form.

Find the slope of the line. y=17x+29y = 17 x + 29y=17x+29

Graph the equation. y=x2+2xy = x ^ { 2 } + 2 xy=x2+2x

Use point-slope form to write the equation of the line.

Indicate the quadrant in which the point (- 9, - 2) lies.

Write the equation of the line that passes through the point P(0,0) P ( 0,0 ) P(0,0) and is perpendicular to the line y=−y = -y=− 4x+104 x + 104x+10 .

True or False? The points A,B,CA , B , CA,B,C and DDD are vertices of a square. A(4,2);B(6,3);C(5,5);D(3,4)A ( 4,2 ) ; B ( 6,3 ) ; C ( 5,5 ) ; D ( 3,4 )A(4,2);B(6,3);C(5,5);D(3,4)

Find the slope of the line through $P ( - 8,8 )$ and $Q ( 1 , - 37 )$ .

Find the midpoint of the line segment $P Q$ . $P ( 10,3 ) , Q ( 4,9 )$

Draw the line using the slope and $y$ -intercept. $y + 1 = 2 x$

Determine whether the line through the points $P ( 8,34 ) , Q ( 12,16 )$ and the line through $R ( 4,17 ) , S ( 6,8 )$ are parallel, perpendicular, or neither.

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

Find the slope of the line. $11 x - 3 = 10 ( y + x )$

Find the equation of the line parallel to the line $x = 3$ and passing through the midpoint of the segment joining $( 9,3 )$ and $( 5 , - 1 )$ .

Find the graph of the equation. $3 x - y = 2$

Find the slope of the line. $2 ( x - 16 ) = 25 y + 21$

Write the equation of the line that passes through the point $P ( 0,0 )$ and is parallel to the line $y = 10 x - 9$ .

Find the x-intercept of the function. $5 x + 13 y = 15$

Graph the equation. $y = 4 - | x |$

Use the slope-intercept form to write the equation of the line passing through the point $P ( 24,2 )$ and having the slope $m = - \frac { 1 } { 2 }$ . Express the answer in general form.

Find the slope of the line. $y = 17 x + 29$

Graph the equation. $y = x ^ { 2 } + 2 x$

Use point-slope form to write the equation of the line. $Use point-slope form to write the equation of the line. A) \quad y = 4 x + 6 B) \quad y = 4 x + 7 C) y = 4 x - 6 D) \quad y = 6 x + 4 E) none of these$

Write the equation of the line that passes through the point $P ( 0,0 )$ and is perpendicular to the line $y = -$ $4 x + 10$ .

True or False? The points $A , B , C$ and $D$ are vertices of a square. $A ( 4,2 ) ; B ( 6,3 ) ; C ( 5,5 ) ; D ( 3,4 )$