Deck 3: Linear Equations in Two Variables

Question 1

Find the slope and y-intercept (if possible)of the equation of the line.Select the correct answer for the line.? $$3 y + 6 = 0$$ ?

A) ?m = 0
Y-intercept: (0,-2)
B) ?m = 0
There is no y-intercept.
C) m = -6
Y-intercept: (0,3)
D) ?m = -3
Y-intercept: (0,6)
E)? ?m is undefined.y-intercept: (0,-2)

Answer 1

?m = 0
Y-intercept: (0,-2)

Question 2

Find the slope of the line passing through the pair of points. ?
(8,-4), (1,-4)
?

A) m = 0
B) m = - $\frac { 1 } { 8 }$
C) m = $- \frac { 8 } { 9 }$
D) m is undefined
E) m = $\frac { 1 } { 8 }$

Answer 2

m = 0

Question 3

Find the slope and y-intercept (if possible)of the equation of the line.Select the correct answer for the line.? $$y = x - 3$$ ?

A)? m = -1
Y-intercept: (0,3)
B) m = 1
Y-intercept: (0,-3)
C) ? m is undefined.y-intercept: (0,3)
D)? m = 3
Y-intercept: (0,3)
E)? m = -3
Y-intercept: (0,-3)

Answer 3

m = 1
Y-intercept: (0,-3)

Question 4

Find the slope-intercept form of the equation of the line that passes through the given point and has the indicated slope m.Select correct answer for the line.? $$\mathrm { P } ( 0,0 ) , m = 2$$ ?

A) $$y = 2 x - 2$$ ?
B) $$y = 2 x + 2$$ ?
C) $$y = - 2 x$$
D) $$y = - 2 x - 2$$
E) $$y = 2 x$$

Question 5

Find the slope of the line passing through the pair of points. ?
(0,-8), (-6,0)
?

A) m = $\frac { 4 } { 3 }$
B) m = $\frac { 4 } { 3 }$
C) m = - $\frac { 4 } { 3 }$
D) m = $\frac { 2 } { 3 }$
E) m = - $\frac { 4 } { 3 }$

Question 6

Find the slope and y-intercept (if possible)of the equation of the line.Select the correct answer for the line.? $$3 x - 5 = 0$$ ?

A) ?m is undefined.There is no y-intercept.
B) ?m = -3
Y-intercept: (0,5)
C) ?m is undefined.There is no y-intercept.
D) ?m = -5
Y-intercept: (0,3)
E)? ?m is undefined.There is no y-intercept.

Question 7

Find the slope of the line passing through the pair of points. ?
(10,12), (12,-12)
?

A) m = -12
B) m = -12
C) m = $\frac { 19 } { 14 }$
D) m = $\frac { 19 } { 14 }$
E) m = $\frac { 6 } { 5 }$

Question 8

Find the slope and y-intercept (if possible)of the equation of the line.Select the correct answer for the line.? $$y + 4 = 0$$ ?

A) ?m = 0
Y-intercept: (0,4)
B) ?m = 0
Y-intercept: (0,-4)
C) ?m is undefined.There is no y-intercept.
D) ?m = 0
Y-intercept: (0,-4)
E) ? ?m = 0
There is no y-intercept.

Question 9

Find the slope of the line passing through the pair of points. ?
(-1,-8), (3,7)
?

A) m = $- \frac { 1 } { 2 }$
B) m = $\frac { 15 } { 4 }$
C) m = - $\frac { 4 } { 15 }$
D) m = - $\frac { 15 } { 4 }$
E) m = $\frac { 4 } { 15 }$

Question 10

Estimate the slope of the line.​ ​

A)5.5
B)3.5
C)4.5
D)6.5
E)Undefined

Question 11

Find the slope and y-intercept (if possible)of the equation of the line.Select the line.? $$y = - \frac { 1 } { 6 } x + 6$$ ?

A) m = -6
Y-intercept: (0,6)
B) ? m is undefined.y-intercept: (0,6)
C)? ? $$m = - \frac { 1 } { 6 }$$
Y-intercept: (0,6)
D) m = -1
Y-intercept: (0,6)
E)? m = 6
Y-intercept: (0,6)

Question 12

Find the slope and y-intercept (if possible)of the equation of the line.Select the correct answer for the line.? $$y = 8 x + 1$$ ?

A)? m = -8
Y-intercept: (0,1)
B)? m = -1
Y-intercept: (0,1)
C)? m is undefined.y-intercept: (0,1)
D)? m = 1
Y-intercept: (0,1)
E) ? m = 8
Y-intercept: (0,1)

Question 13

Find the slope of the line passing through the pair of points. ?
(14,0), (0,-3)
?

A) m = $- \frac { 1 } { 16 }$
B) m = $\frac { 14 } { 3 }$
C) m = $\frac { 3 } { 14 }$
D) m = - $\frac { 3 } { 14 }$
E) m = - $\frac { 14 } { 3 }$

Question 14

Find the slope and y-intercept (if possible)of the equation of the line.Select the correct answer for the line.? $$x + 3 = 0$$ ?

A) m = -3
Y-intercept: (0,2)
B) m is undefined.There is no y-intercept.
C) ?m = -2
Y-intercept: (0,3)
D) ? m is undefined.There is no y-intercept.
E)? m is undefined.There is no y-intercept.

Question 15

Find the slope-intercept form of the equation of the line that passes through the given point and has the indicated slope m.Select the correct answer for the line. ?
P(3,-7),m is undefined.
?

A) $$x = 3 y - 7$$
B) $$y = 3$$ ?
C) $$x = - 7$$
D) $$x = 3$$ ?
E) $$y = 3 x - 7$$

Question 16

Find the slope-intercept form of the equation of the line that passes through the given point and has the indicated slope m.Select correct answer for the line.? $$\mathrm { P } ( - 7,6 ) , m = - 3$$ ?

A) $$y = 6 x + 6$$
B) $$y = 6 x - 6$$
C) $$y = - 3 x - 15$$ ?
D) $$y = - 7 x - 7$$
E) $$y = 6 x + 6$$ ?

Question 17

Find the slope-intercept form of the equation of the line that passes through the given point and has the indicated slope m.Select correct answer for the line. ?
P(0,-7),m = 8
?

A) $y = - 8 x + 8$ ?
B) $y = - 7 x - 7$
C) $$y = 8 x - 8$$ ?
D) $$y = 8 x - 7$$ ?
E) $$y = 8 x + 8$$ ? ?

Question 18

Find the slope of the line passing through the given pair of points. ?
(0,9), (2,0)
?

A) m = - $\frac { 2 } { 9 }$
B) m = $\frac { 9 } { 2 }$
C) m = - $\frac { 9 } { 2 }$
D) m = $\frac { 4 } { 11 }$
E) m = - $\frac { 9 } { 2 }$

Question 19

Find the slope and y-intercept (if possible)of the equation of the line.Select the correct answer for the line.? $$y - 3 = 0$$ ?

A) m = -3
Y-intercept: (0,-3)
B) m = 0
Y-intercept: (0,3)
C) m is undefined.There is no y-intercept.
D) m = 0
There is no y-intercept.
E)? m = 0
There is no y-intercept.

Question 20

Find the slope of the line passing through the pair of points. ​
(4)1,3.1), (-3.8,3.1)
​

A) m = 0.40
B) m = -Infinity
C) m = 0.80
D) m = 0.00
E) m = 20.67

Question 21

Determine whether the lines are parallel,perpendicular,or neither. ?
L1: y = $\frac { 9 } { 2 }$ x - 9
L2: y = - $\frac { 2 } { 9 }$ x - 2
?

A)Perpendicular
B)Neither
C)Parallel

Question 22

Find the slope-intercept form of the equation of the line passing through the points.Select the correct answer for the line.? $$\mathrm { P } ( 6,4 ) , \mathrm { Q } ( - 6 , - 6 )$$ ?

A)y = $\frac { 5 } { 6 }$ x+1
B)y = $\frac { 5 } { 6 }$ x-6
C)y = $\frac { 6 } { 5 }$ x-2
D)y = $\frac { 5 } { 6 }$ x-1
E)y = - $\frac { 5 } { 6 }$ x-2

Question 23

Use the intercept form to find the equation of the line with the given intercepts.The intercept form of the equation of a line with intercepts (a,0)and (0,b)is? $\frac { x } { a } + \frac { y } { b } = 1 , a \neq 0 , b \neq 0$ ? ?
X-intercept: ( $- \frac { 5 } { 8 }$ ,0)
Y-intercept: $( 0 , - 3 )$ ?
?

A) $- 24 x - 8 y - 5 = 0$
B) $24 x + 8 y - 5 = 0$
C) $- 24 x + 8 y + 5 = 0$
D) $24 x + 5 y + 15 = 0$
E) $24 x - 8 y + 5 = 0$

Question 24

The graph shows the sales (in billions of dollars)for Apple Inc.for the years 2001 through 2007.​ Find the slope of the line segment connecting the points for the years 2003 and 2004.Round the answer to two decimal places. ​

A)-5.07
B)2.07
C)7.07
D)3.07
E)-2.07

Question 25

The following is the slope of line representing annual sale y in term of time x in year.Use the slope to interpret any change in annual sales for a one-year increase in time. ​
The line has a slope of m = 134.
​

A)No change in sales
B)Sales decreasing 134 units/yr
C)Sales increasing 134 units/yr
D)None of the above

Question 26

Use the intercept form to find the equation of the line with the given intercepts.The intercept form of the equation of a line with intercepts (a,0)and (0,b)is ?? $\frac { x } { a } + \frac { y } { b } = 1 , a \neq 0 , b \neq 0$ ?
X-intercept: (-3,0)
Y-intercept: (0,8)
?
?

A) $$- 3 x + 8 y + 24 = 0$$
B) $8 x + 3 y + 24 = 0$
C) $8 x - 3 y + 24 = 0$
D) $8 x - 3 y - 24 = 0$
E) $- 3 x + 8 y - 24 = 0$

Question 27

Estimate the slope of the line.​ ​

A)-2
B)-3
C)-4
D)-1
E)Undefined

Question 28

You are driving on a road that has a 5% uphill grade.This means that the slope of the road is $$\frac { 5 } { 100 }$$ .Approximate the amount of vertical change in your position if you drive 400 feet. ?

A)18 ft
B)21 ft
C)22 ft
D)19 ft
E)20 ft

Question 29

A sub shop purchases a used pizza oven for $885.After 5 years,the oven will have to be replaced.Select the linear equation giving the value V of the equipment during the 5 years it will be in use. ?

A) $V = - 177 + 885 t$
B) $V = - 177 t - 885$
C) $V = 177 t - 885$
D) $V = 177 t + 885$
E) $V = - 177 t + 885$ ?

Question 30

Use the intercept form to find the equation of the line with the given intercepts.The intercept form of the equation of a line with intercepts (a,0)and (0,b)is ?? $\frac { x } { a } + \frac { y } { b } = 1 , a \neq 0 , b \neq 0$ ?
X-intercept: $\left( - \frac { 1 } { 6 } , 0 \right)$ y-intercept: $\left( 0 , - \frac { 2 } { 7 } \right)$ ?
?

A) $12 x - 7 y + 2 = 0$
B) $- 12 x + 7 y + 2 = 0$
C) $12 x + 7 y + 2 = 0$
D) $- 7 x - 12 y - 2 = 0$
E) $12 x + 7 y - 2 = 0$

Question 31

Determine whether the lines are parallel,perpendicular,or neither. ?
L1: y = $\frac { 1 } { 2 }$ x - 4
L2: y = - $\frac { 1 } { 2 }$ x - 2
?

A)Parallel
B)Perpendicular
C)Neither

Question 32

Use the intercept form to find the equation of the line with the given intercepts.The intercept form of the equation of a line with intercepts (a,0)and (0,b)is $\frac { x } { a } + \frac { y } { b } = 1 , a \neq 0 , b \neq 0$ ?? Point on line: (4,6)
X-intercept: (c,0)
Y-intercept: (0,c),c ? 0
?
?

A) $x + y + 10 = 0$
B) $x + y - 10 = 0$
C) $- x + y - 10 = 0$
D) $x - y - 10 = 0$
E) $- x - y - 10 = 0$

Question 33

The following is the slope of line representing annual sale y in term of time x in year.Use the slope to interpret any change in annual sales for a one-year increase in time. ​
The line has a slope of m = -20.
​

A)Sales increasing 20 units/yr
B)Sales decreasing 20 units/yr
C)No change in sales
D)None of the above

Question 34

Find the slope-intercept form of the equation of the line that passes through the given point and has the indicated slope m.Select correct answer for the line. ?
P(4, $$\frac { 8 } { 7 }$$ ),m = 0
?

A) $$y = 4$$ ?
B)y = 4x + $$\frac { 8 } { 7 }$$
C)y = $$\frac { 8 } { 7 }$$ ?
?
D)x = 4y + $$\frac { 8 } { 7 }$$
E) $$x = 4$$

Question 35

Use the intercept form to find the equation of the line with the given intercepts.The intercept form of the equation of a line with intercepts (a,0)and (0,b)is? $\frac { x } { a } + \frac { y } { b } = 1 , a \neq 0 , b \neq 0$ . ?
X-intercept: (3,0)
Y-intercept: (0,9)
?

A) $3 x + 9 y - 27 = 0$
B) $9 x + 3 y - 27 = 0$
C) $3 x + 9 y + 27 = 0$
D) $9 x + 3 y + 27 = 0$
E) $$9 x - 3 y - 27 = 0$$

Question 36

Find the slope-intercept form of the equation of the line passing through the points.Select the correct answer for the line.? $$P ( 6 , - 2 ) , Q ( - 6,6 )$$ ?

A)y = $$- \frac { 2 } { 3 }$$ x-2
B)y = $$- \frac { 3 } { 2 }$$ x-6
C)y = $$- \frac { 2 } { 3 }$$ x+2
D)y = $$- \frac { 2 } { 3 }$$ x-4
E)y = $$- \frac { 2 } { 3 }$$ x+6

Question 37

The graph shows the average salaries for senior high school principals from 1996 through 2008.​ ​ Find the slope of the line segment connecting the points for the years 1998 and 2002.
​

A)-2394
B)2391
C)-2391
D)2396
E)2392

Question 38

Find the slope-intercept form of the equation of the line that passes through the given point and has the indicated slope m.Select correct answer for the line. ​
P(2)4,-8.7),m = -4
​

A)x = 2.4y + 0.9
B)x = 2.4
C)y = 2.4 ​
D)y = -4x + 0.9 ​
E)y = 2.4x + 0.9

Question 39

The following is the slope of line representing daily revenue y in term of time x in day.Use the slope to interpret any change in daily revenues for a one-day increase in time. ​
The line has a slope of m = 500.
​

A)Revenues increasing 500 units/day
B)No change in revenues
C)Revenues decreasing 500 units/day
D)None of the above

Question 40

Determine whether the lines are parallel,perpendicular,or neither. ?
L1: y = $\frac { 1 } { 3 }$ x - 4
L2: y = $\frac { 1 } { 3 }$ x - 3
?

A)Perpendicular
B)Parallel
C)Neither

Question 41

Find the y-intercept of the line determined by the equation.? $$- 7 x + 4 y = 3$$ ?

A) $\left( 0 , \frac { 7 } { 4 } \right)$
B) $\left( 0 , \frac { 3 } { 4 } \right)$
C) $\left( 0 , - \frac { 3 } { 4 } \right)$
D) $\left( - \frac { 7 } { 4 } , 0 \right)$
E) $\left( 0 , - \frac { 7 } { 4 } \right)$

Question 42

A sales representative of a company using a personal car receives $160 per day for lodging and meals plus $0.53 per mile driven.Select a linear equation giving the daily cost C to the company in terms of x,the number of miles driven. ?

A) $C = 0.53 + 160 x$
B) $C = 0.53 x + 160$
C) $C = - 0.53 x - 160$
D) $C = 0.53 x - 160$
E) $C = - 0.53 x + 160$

Question 43

Write the slope-intercept form of the equation of the line through the given point perpendicular to the given line. point: (-4,9) line: 6x - 30y = 6

A)? $y = - \frac { 1 } { 6 } x + \frac { 1 } { 3 }$
B)? $y = - 5 x - \frac { 4 } { 5 }$
C)? $y = - 5 x - 11$
D)? $y = 6 x - 15$
E)? $y = \frac { 1 } { 5 } x + \frac { 4 } { 5 }$

Question 44

Find the slope of the line passing through the pair of points. ​
P(5,4);Q(9,20).​
​

A)m = 5
B)m = 4
C)m = 2
D)m = 3
E)m = 6

Question 45

A microchip manufacturer pays its assembly line workers $12.25 per hour.In addition,workers receive a piecework rate of $0.3 per unit produced.Select a linear equation for the hourly wage W in terms of the number of units x produced per hour. ?

A) $W = 0.3 x + 12.25$
B) $W = 0.3 x - 12.25$
C) $W = 12.25 x + 0.3$
D) $W = 12.25 x - 0.3$
E) $W = 12.55 x$

Question 46

Find the slope of the line passing through the pair of points. ?
P (-9,14);Q (-18,-2)
?

A)m = $\frac { 16 } { 9 }$
B)m = - $\frac { 9 } { 16 }$
C)m = - $\frac { 16 } { 9 }$
D)m = $\frac { 9 } { 16 }$
E)none of these

Question 47

Find the slope of the line. ​
Y = 9x + 25
​

A)m = -9
B)m = 10
C)m = 13
D)m = 9
E)m = 6

Question 48

A real estate office handles an apartment complex with 60 units.When the rent per unit is $98 per month,all 60 units are occupied.However,when the rent is $630 per month,the average number of occupied units drops to 46.Assume that the relationship between the monthly rent p and the demand x is linear. Select the equation of the line giving the demand x in terms of the rent p.
?

A)x = 532p + 62.58
B)x = -38p - 62.58
C)x = $- \frac { 1 } { 38 }$ p + 62.58
D)x = -38p + 62.58
E)x = 14p + 62.58

Question 49

Find the slope of the line passing through the pair of points.? $\mathrm { P } ( 19 , \sqrt { 2 } ) ; \mathrm { Q } ( \sqrt { 2 } , 19 )$ ?

A)m = 19
B)m = 1
C)m = 2
D)m = -1
E)none of these

Question 50

Write the equation of the line that passes through the point P (0,0)and is perpendicular to the line y = - 2x + 10. ?

A) $y = \frac { 1 } { 2 } x$
B) $y = - \frac { 1 } { 10 } x$
C) $y = - 10 x$
D) $y = 2 x$
E) $y = - \frac { 1 } { 2 } x + 10$

Question 51

The length and width of a rectangular garden are 16 meters and 11 meters,respectively.A walkway of width x surrounds the garden. ?Write the equation for the perimeter y of the walkway in terms of x.
?

A) $y = 8 x + 54$
B) $y = 8 x - 54$
C) $y = 8 x + 27$
D) $y = 4 x + 54$
E) $y = 4 x + 27$

Question 52

Write the equation of the line that passes through the point P(0,0)and is parallel to the line y = 8x - 7. ​

A)x = 8y
B)y = 7x +8
C)y = -7x
D)y = 8x
E)y = 7x

Question 53

Find the slope of the line determined by the equation.? $9 x + 10 y = 11$ ?

A) $m = - 9$
B) $m = 9$
C) $m = - \frac { 9 } { 10 }$
D) $m = \frac { 11 } { 10 }$
E) $m = - 10$

Question 54

A pharmaceutical salesperson receives a monthly salary of $2600 plus a commission of 2% of sales.Select a linear equation for the sales-person's monthly wage W in terms of monthly sales S. ?

A) $W = - 0.02 S + 2600$
B) $W = - 0.02 S - 2600$
C) $W = 0.02 S + 2600$
D) $S = 0.02 W - 2600$
E) $S = 0.02 W + 2600$

Question 55

Carl's Tractor Service purchases a used brush mower for $1445.The machine has a useful life of 5 years after which time another one will have to be purchased.Assume depreciation of the machine is linear.Write a linear equation giving the value V of the used brush mower during the 5 years it will be in use.

A) $V = - \frac { 1 } { 289 } t - 1445$
B) $V = 289 t - 1445$
C) $V = - \frac { 1 } { 289 } t + 5$
D) $V = \frac { 1 } { 289 } t + 5$
E) $V = - 289 t + 1445$ ?

Question 56

A school district purchases a high-volume printer,copier,and scanner for $20,000. After 10 years,the equipment will have to be replaced.Its value at that time is expected to be $2,600.Select a linear equation giving the value of the equipment during the 10 years it will be in use.
?

A) $V = 1740 t - 20,000$
B) $V = - 1740 t - 20,000$
C) $V = 1740 t + 20,000$
D) $V = - 1740 t + 20,000$
E) $V = - 1740 + 20,000 t$

Question 57

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

A) ​
B) ​
C) ​
D) ​

Question 58

Find the slope of the line passing through the pair of points. ​
P(-4,3);Q(2,-9).
​

A)m = 1
B)m = -7
C)m = 4
D)m = -2
E)m = -1

Question 59

A discount outlet is offering a 70% discount on all items.Select a linear equation giving the sale price S for an item with a list price L. ?

A) $$L = 0.3 S$$
B) $L = 0.7 S$
C) $S = 0.7 L$
D) $$S = 70 L$$
E) $S = 0.3 L$

Question 60

Write the equation of the line that passes through the point P(4,3)and is perpendicular to the line y = - 5x + 2. ?

A) $y = \frac { 1 } { 5 } x + 2$ ?
B) $y = \frac { 1 } { 5 } x + 3.8$
C) $y = \frac { 1 } { 5 } x + 2.2$
D) $y = 2.2 x + \frac { 1 } { 5 }$
E) $y = x + 2.2$

Question 61

Find the slope of the line through P(-8,-5)and Q(2,35).