Deck 3: The Rectangular Coordinate System and Graphs of Equations

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. $\quad m = - 6$

Answer 1

D

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. $M ( 7,6 )$

Answer 2

E

Question 3

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

b.

c.

d.

Answer 3

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

Question 5

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

b.

c.

d.

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. $m = \frac { 11 } { 10 }$

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 $( 5 , - 1 )$ .
$\begin{array} { l l } \text { a. } \quad & y = 1 \\ \text { b. } & x = 0 \end{array}$
b. $\quad x = 9$
c. $\quad x = 7$
d. $\quad y = - 5$
e. $\quad x = 4$

Question 8

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

b.

C.

d.

e.

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. $\quad \$ 570.00$
b. $\$ 382.50$
c. $\$ 420.00$
$\begin{array} { l l } \text { d. } & \$ 195.00 \\ \text { e. } & \$ 375.00 \end{array}$

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. $m = 2$

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. $\quad y = 9 x$

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. $\quad ( 15 / 13,0 )$

Question 13

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

b.

C.

d.

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. $x - 2 y = 28$

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. $\quad m = - 17$

Question 16

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

b.

c.

d.

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

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

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

Question 20

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

Question 21

Find the midpoint of the line segment $P Q$ .
$P ( 4,9 ) , Q ( 8,7 )$
a. $\quad M ( 11,11 )$
b. $M ( 1,0 )$
c. $M ( 6,8 )$
d. $M ( 8,8 )$
e. $M ( 6,7 )$

Question 22

Find the x-intercept of the function. $$9 x + 8 y = 16$$
a. $( 9 / 16,0 )$
b. $\quad ( 0,2 )$
c. $( 2,0 )$
d. $\quad ( 0,16 / 9 )$
e. $( 16 / 9,0 )$

Question 23

Find the slope of the line through $P ( 2 , - 2 )$ and $Q ( 6 , - 18 )$ .
a. $\quad m = - 5$
b. $\quad m = - 4$
c. $\quad m = - 6$
d. $\quad m = - 3$
e. $\quad m = - 2$

Question 24

Write the equation of the line that passes through the point $P ( 0,0 )$ and is perpendicular to the line $y =$ $10 x + 5$ .
a. $y = - \frac { 1 } { 5 } x$
b. $y = - 5 x$
c. $y = 10 x$
d. $\quad y = \frac { 1 } { 10 } x$
e. $\quad y = - \frac { 1 } { 10 } x + 5$

Question 25

Find the slope of the line. $11 x - 27 = 10 ( y + x )$
a. $\quad m = \frac { 27 } { 11 }$
b. $m = - \frac { 1 } { 10 }$
c. $m = \frac { 11 } { 10 }$
d. $m = 11$
e. $m = \frac { 1 } { 10 }$
f. $m = 10$

Question 26

Write the equation of the line that passes through the point $P ( 0,0 )$ and is parallel to the line $y = 5 x - 3$ .
a. $\quad y = 3 x + 5$
b. $\quad x = 5 y$
c. $\quad y = 5 x$
d. $y = - 3 x$
e. $y = 3 x$

Question 27

Solve the proportion. $$\frac { x } { 21 } = \frac { 2 } { x + 1 }$$
a. $\quad x _ { 1 } = - 7 , x _ { 2 } = - 6$
b. $\quad x _ { 1 } = - 7 , x _ { 2 } = 6$
c. $\quad x _ { 1 } = 7 , x _ { 2 } = 6$
d. $\quad x _ { 1 } = 7 , x _ { 2 } = - 6$
e. no solutions

Question 28

Find the slope of the line. $$6 ( x - 25 ) = 25 y + 17$$
a. $m = 25$
b. $m = \frac { 25 } { 25 }$
c. $m = \frac { 8 } { 25 }$
d. $\quad m = 6$
e. $m = \frac { 6 } { 25 }$
f. $m = - \frac { 6 } { 25 }$

Question 29

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

b.

C.

d.

e.

Question 30

Find the constant of proportionality for the stated conditions: $E$ varies jointly with $I$ and $R$ , and when $E$ $= 2,520 , R = 40$ and $\mathrm { I } = 7$ .
a. $\quad k = 7$
b. $k = 9$
c. $\quad k = - 9$
d. $\quad k = - 2,520$
e. $\quad k = 2,520$

Question 31

Use point-slope form to write the equation of the line.
a. $y = 2 x + 1$
b. none of these
c. $y = 2 x + 2$
d. $y = 2 x - 1$
e. $y = 1 x + 2$

Question 32

Use the slope-intercept form to write the equation of the line passing through the point $P ( 28,0 )$ and having the slope $m = - \frac { 1 } { 2 }$ . Express the answer in general form.
a. $\quad x - 2 y = - 14$
b. $\quad x - 2 y = 28$
c. $\quad x + 2 y = 28$
d. $\quad y = \frac { 1 } { 2 } x + 1$
e. $\quad x + 2 y = - 28$

Question 33

Find the slope of the line. $$y = 12 x + 10$$
a. $\quad m = 13$
b. $\quad m = 16$
c. $\quad m = - 12$
d. $\quad m = 9$
e. $\quad m = 12$

Question 34

Decide which type of variation the graph represents.

A)direct variation
B)neither
C)inverse variation

Question 35

Determine whether the line through the points $P ( 40,18 ) , Q ( 26,20 )$ and the line through $R ( 20,9 )$ , $S ( 13,10 )$ are parallel, perpendicular, or neither.
a. neither
b. perpendicular
c. parallel

Question 36

Indicate the quadrant in which the point (- 5, - 2) lies. a. none of these
b. quadrant III
c. quadrant II
d. quadrant I
e. quadrant IV

Question 37

For what value of $a$ does the equation $x ^ { 2 } + y ^ { 2 } - a x + 6 y + 33 = 0$ represent a circle with center $( 7 , - 3 )$ ? When $a$ assumes this value, what is the radius of the circle?
a. $\quad a = 14$ , radius $= 5$
b. $\quad a = 13 , \quad$ radius $= 4$
c. $\quad a = 13$ , radius $= 6$
d. $\quad a = 15 , \quad$ radius $= 7$
e. $\quad a = 12 , \quad$ radius $= 6$

Question 38

True or False? The points $A , B , C$ and $D$ are vertices of a square.
$$A ( 6,4 ) ; B ( 8,5 ) ; C ( 7,7 ) ; D ( 5,6 )$$

Question 39

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

b.

c.

d.

Question 40

The power, in watts, dissipated as heat in a resistor varies jointly with the resistance, in ohms, and the square of the current, in amperes.A 15-ohm resistor carrying a current of 1 ampere dissipates 15 watts.
How much power is dissipated in a 80-ohm resistor carrying a current of 3 amperes? a. $\quad P = 80 \mathrm { Watts }$
b. $\quad P = 8$ Watts
c. $P = 3$ Watts
d. $P = 720 \mathrm { Watts }$
e. $P = 24 \mathrm { Watts }$

Question 41

Find the x-intercept of the function. $$5 x + 4 y = 13$$
a. $\quad ( 5 / 13,0 )$
b. $( 13 / 5,0 )$
c. $( 13 / 4,0 )$
d. $( 0,13 / 4 )$
e. $( 0,13 / 5 )$

Question 42

Indicate the quadrant in which the point $( - 6 , - 1 )$ lies.
a. quadrant III
b. quadrant II
c. quadrant I
d. quadrant IV
e. none of these

Question 43

Solve the proportion. $$\frac { x } { 18 } = \frac { 4 } { x + 1 }$$
a. $\quad x _ { 1 } = - 9 , x _ { 2 } = 8$
b. $\quad x _ { 1 } = 9 , x _ { 2 } = 8$
c. $\quad x _ { 1 } = - 9 , x _ { 2 } = - 8$
d. $\quad x _ { 1 } = 9 , x _ { 2 } = - 8$
e. no solutions

Question 44

Graph the equation. $$y = x ^ { 2 } + 3 x$$
a.

b.

c.

d.

Question 45

The power, in watts, dissipated as heat in a resistor varies jointly with the resistance, in ohms, and the square of the current, in amperes.A 10-ohm resistor carrying a current of 1 ampere dissipates 10 watts.
How much power is dissipated in a 50-ohm resistor carrying a current of 9 amperes? a. $\quad P = 50$ Watts
b. $P = 45 \mathrm { Watts }$
c. $P = 9 \mathrm { Watts }$
d. $P = 4,050 \mathrm { Watts }$
e. $P = 5$ Watts

Question 46

$$\text { Find the midpoint of the line segment } P Q \text {. }$$ $P ( 4,7 ) , Q ( 2,5 )$
a. $\quad M ( 1,0 )$
b. $\quad M ( 3,6 )$
c. $\quad M ( 5,6 )$
d. $\quad M ( 8,9 )$
e. $\quad M ( 3,5 )$

Question 47

Find the slope of the line. $2 ( x - 16 ) = 25 y + 22$
a. $m = \frac { 4 } { 25 }$
b. $\quad m = 25$
c. $m = 2$
d. $m = - \frac { 2 } { 25 }$
e. $m = \frac { 2 } { 25 }$
f. $m = \frac { 16 } { 25 }$

Question 48

Graph the equation. $$y = 5 | x |$$
a.

b.

c.

d.

Question 49

Find the slope of the line. $17 x - 5 = 15 ( y + x )$
a. $\quad m = 17$
b. $\quad m = 15$
c. $\quad m = \frac { 17 } { 15 }$
d. $m = - \frac { 2 } { 15 }$
e. $m = \frac { 2 } { 15 }$
f. $m = \frac { 5 } { 17 }$

Question 50

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

Question 51

Find the slope of the line. $$y = 11 x + 16$$
a. $\quad m = 11$
b. $\quad m = 15$
c. $m = - 11$
d. $\quad m = 8$
e. $m = 12$

Question 52

Find the constant of proportionality for the stated conditions: $E$ varies jointly with $I$ and $R$ , and when $E$ $= 3,600 , R = 50$ and $\mathrm { I } = 9$ .
a. $\quad k = - 3,600$
b. $\quad k = 3,600$
c. $\quad k = 8$
d. $\quad k = 9$
e. $k = - 8$

Question 53

Find the equation of the line parallel to the line $x = 2$ and passing through the midpoint of the segment joining $( 1,11 )$ and $( 7 , - 5 )$ .
a. $\quad y = - 7$
b. $\quad x = - 6$
c. $\quad x = 4$
d. $\quad x = 1$
e. $\quad y = 3$

Question 54

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

b.

C.

d.

e.

Question 55

Decide which type of variation the graph represents.
a. direct variation
b. inverse variation
c. neither

Question 56

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

b.

c.

d.

Question 57

For what value of $a$ does the equation $x ^ { 2 } + y ^ { 2 } - a x + 8 y + 16 = 0$ represent a circle with center $( 5 , - 4 ) ?$ When $a$ assumes this value, what is the radius of the circle?
a. $\quad a = 9 , \quad$ radius $= 6$
b. $\quad a = 10 , \quad$ radius $= 5$
c. $\quad a = 8 , \quad$ radius $= 6$
d. $\quad a = 9 , \quad$ radius $= 4$
e. $\quad a = 11$ , radius $= 7$

Question 58

Determine whether the line through the points $P ( 4,30 ) , Q ( 8,14 )$ and the line through $R ( 2,15 ) , S ( 4,7 )$ are parallel, perpendicular, or neither.
a. neither
b. perpendicular
c. parallel

Question 59

Find the slope of the line through $P ( - 4 , - 1 )$ and $Q ( - 1 , - 19 )$ .
a. $\quad m = - 4$
b. $\quad m = - 7$
c. $\quad m = - 8$
d. $\quad m = - 6$
e. $\quad m = - 5$

Question 60

In the following exercise, assume straight-line depreciation. A word processor costs $\$ 565.00$ when new and is expected to be worth $\$ 115.00$ after 5 years. What will it be worth after 2 years?
a. $\quad \$ 115.00$
b. $\quad \$ 340.00$
c. $\quad \$ 385.00$
d. $\quad \$ 565.00$
e. $\quad \$ 450.00$

Question 61

For what value of $a$ does the equation $x ^ { 2 } + y ^ { 2 } - a x + 4 y + - 3 = 0$ represent a circle with center $( 3 , - 2 )$ ? When $a$ assumes this value, what is the radius of the circle?
a. $\quad a = 4 , \quad$ radius $= 5$
b. $\quad a = 7 , \quad$ radius $= 6$
c. $\quad a = 6 , \quad$ radius $= 4$
d. $\quad a = 5 , \quad$ radius $= 5$
e. $\quad a = 5 , \quad$ radius $= 3$

Question 62

Graph the equation. $$y = 6 - | x |$$
$\mathrm { a } .$

b.

c.

d.

Question 63

Graph the equation. $$y = 5 | x |$$
$\mathfrak { a }$

b.

c.

d.

Question 64

Use the slope-intercept form to write the equation of the line passing through the point $P ( 16,0 )$ and having the slope $m = - \frac { 1 } { 4 }$ . Express the answer in general form.
a. $\quad x - 4 y = - 12$
b. $\quad x + 4 y = 16$
c. $\quad x + 4 y = - 16$
d. $\quad y = \frac { 1 } { 4 } x + 1$
e. $x - 4 y = 16$

Question 65

The power, in watts, dissipated as heat in a resistor varies jointly with the resistance, in ohms, and the square of the current, in amperes.A 30-ohm resistor carrying a current of 1 ampere dissipates 30 watts.
How much power is dissipated in a 50-ohm resistor carrying a current of 8 amperes? a. $\quad P = 50$ Watts
b. $\quad P = 8$ Watts
c. $\quad P = 3,200$ Watts
d. $P = 5$ Watts
e. $P = 40$ Watts

Question 66

Solve the proportion. $$\frac { x } { 24 } = \frac { 2 } { x + 2 }$$
a. $\quad x _ { 1 } = - 8 , x _ { 2 } = - 6$
b. $x _ { 1 } = 8 , x _ { 2 } = - 6$
c. no solutions
d. $\quad x _ { 1 } = - 8 , x _ { 2 } = 6$
e. $\quad x _ { 1 } = 8 , x _ { 2 } = 6$

Question 67

Find the equation of the line parallel to the line $x = 10$ and passing through the midpoint of the segment joining $( 9,7 )$ and $( 5 , - 3 )$ .
a. $\quad y = 2$
b. $x = 7$
c. $x = 9$
d. $\quad x = 4$
e. $\quad y = - 5$

Question 68

Use point-slope form to write the equation of the line.
a. $\quad y = 2 x + 4$
b. none of these
c. $y = 3 x + 2$
d. $y = 2 x + 3$
e. $y = 2 x - 3$

Question 69

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. $\quad y = 10 x$
b. $\quad y = - 9 x$
c. $\quad y = 9 x$
d. $\quad x = 10 y$
e. $y = 9 x + 10$

Question 70

Find the constant of proportionality for the stated conditions: $E$ varies jointly with $I$ and $R$ , and when $E$ $= 500 , R = 50$ and $\mathrm { I } = 2$ .
a. $\quad k = - 5$
b. $\quad k = - 500$
c. $\quad k = 500$
d. $\quad k = 2$
e. $\quad k = 5$

Question 71

Graph the equation. $$y = x ^ { 2 } + 5 x$$
a.

b.

c.

d.

Question 72

Decide which type of variation the graph represents.
a. neither
b. direct variation
c. inverse variation

Question 73

Write the equation of the line that passes through the point $P ( 0,0 )$ and is perpendicular to the line $y = -$ $10 x + 5$ .
a. $\quad y = 10 x$
b. $\quad y = - \frac { 1 } { 5 } x$
c. $y = - 5 x$
d. $y = - \frac { 1 } { 10 } x + 5$
e. $y = \frac { 1 } { 10 } x$

Question 74

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

b.

c.

d.

Question 75

In the following exercise, assume straight-line depreciation. A word processor costs $\$ 540.00$ when new and is expected to be worth $\$ 165.00$ after 5 years. What will it be worth after 3 years?
a. $\$ 315.00$
b. $\$ 352.50$
c. $\quad \$ 540.00$
d. $\quad \$ 165.00$
e. $\quad \$ 375.00$