Deck 7: Equations and Inequalities in Two Variables

Question 1

Graph the inequality. $$2 x \leq - 3 y - 12$$

A)
B)
C)
D)
E)

Answer 1

Question 2

Determine which of the ordered pairs are solutions to the given equation. $$y = - x + 11$$

A) $( 16 , - 5 ) , ( 2 , - 9 )$
B) $( - 5,16 ) , ( 2,9 )$
C) $( 5,16 ) , ( 2 , - 9 )$
D) $( - 5,9 ) , ( 16,2 )$

Answer 2

$( - 5,16 ) , ( 2,9 )$

Question 3

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

A)
B)
C)
D)
E)

Answer 3

Question 4

Find the coordinates of the point.

A)(-1,-5)
B)(-1,5)
C)(5,1)
D)(1, 5)
E)(-5,1)

Question 5

Graph the equation using the intercept method. Label the intercepts on the graph. $$3 x + 4 y - 8 = 0$$

A)
B)
C)
D)
E)

Question 6

The equation $F = \frac { 9 } { 5 } C + 32$ can be used to convert from degrees in Celsius to degrees in Fahrenheit. Identify the graph of the equation.

A)
B)
C)
D)
E)

Question 7

Use the utility to graph $y = 4 x - 2$ , $4 x - y = 5$ , $y - 3 = 4 x$ and $8 x + 11 = 2 y$ on the same set of axes.

A)
B)
C)
D)

Question 8

The graph of a linear equation is shown below. If the coordinates of point M are substituted into the equation, will the result be true or false? If the coordinates of point N are substituted into the equation, will the result be true or false?

A)true, true
B)false, false
C)false, true
D)true, false
E)none of the above

Question 9

The cost ( c )of playing an online computer game for a time ( t )in hours is given by the equation c = 3 t + 7. Label the horizontal axis t and the vertical axis c , and graph the equation for nonnegative values of t .

A)
B)
C)
D)
E)

Question 10

Use the utility to graph $y = 2 x - 7$ , $y = 1$ and $y = - 3 x - 4$ on the same set of axes.

A)
B)
C)
D)

Question 11

Graph the inequality. $$2 x \geq - y - 4$$

A)
B)
C)
D)
E)

Question 12

Graph the inequality. $y < 5 x - 5$

A)
B)
C)
D)
E)

Question 13

Graph the linear equation. Label the intercepts on the graph. $$x + y = 5$$

A)
B)
C)
D)

Question 14

Graph the equation. $$x + 4 = 0$$

A)
B)
C)
D)
E)

Question 15

Determine which of the ordered pairs are solutions to the given equation. $$2 x - y = 6$$

A)(-1, 5), (0, 3)
B)(2, -10), (1, -5)
C)(-2, -10), (3, 0)
D)(6, 0), (-3, 0)

Question 16

Find the coordinates of the given point:

A)(4, 4)
B)(4, -4)
C)(-4, 4)
D)(-4, -4)

Question 17

Use the utility to obtain a graph of the line $$3.7 y - 1.48 x = 5.55$$ .

A)
B)
C)
D)

Question 18

Determine which of the ordered pairs are solutions to the given equation. $$6 y - 5 x = 18$$

A) $( 3,0 ) , ( 12 , - 13 )$
B) $( 0,13 ) , ( 12,3 )$
C) $( 0 , - 3 ) , ( 12 , - 13 )$
D) $( 0,3 ) , ( 12,13 )$

Question 19

Graph the linear equation. Label the intercepts on the graph. $$4 x - y = 2$$

A)
B)
C)
D)

Question 20

Identify the graph of the equation. 12 x - 4 y = 0

A)
B)
C)
D)
E)

Question 21

Find the equation of the line that contains the given point and has the given slope. Express equation in the form , where A , B , and C are integers.

Question 22

Graph the line that passes through the given point and has the given slope. (0, 0), m = 2

A)
B)
C)
D)

Question 23

Find the distance between the two points. (3, 6)and (-7, -6)

A) $2 \sqrt { 61 }$
B) $4 \sqrt { 61 }$
C)61
D) $\sqrt { 122 }$
E) $\sqrt { 61 }$

Question 24

Find the slope of the line determined by this pair of points. $( a , 0 ) , ( 0 , b )$

A) $- \frac { b } { a }$
B) $\frac { a } { b }$
C) $- \frac { a } { b }$
D) $\frac { b } { a }$
E)undefined

Question 25

Find the equation of the line that contains the two given points. $( 3,1 ) , ( 6,6 )$

A)3 y + 5 x = -12
B)5 x - 3 y = -12
C)3 y - 5 x = -12
D)3 y - 5 x = 18
E)3 y + 5 x = 18

Question 26

The grade of a highway up a hill is 15%. How much change in horizontal distance is there if the vertical height of the hill is 650 feet? Express the answer to the nearest foot.

A)4,352 ft
B)4,333 ft
C)4,233 ft
D)4,343 ft
E)4,308 ft

Question 27

Find the equation of the line with the given slope and y -intercept. $$m = \frac { 2 } { 7 } \text { and } b = 6$$

A) $x = \frac { 2 } { 7 } y + 6$
B) $y = \frac { 2 } { 7 } + 6 x$
C) $y = \frac { 2 } { 7 } - 6 x$
D) $y = \frac { 2 } { 7 } x - 6$
E) $y = \frac { 2 } { 7 } x + 6$

Question 28

Graph the line that passes through the given point and has the given slope. (1, 0), $m = \frac { 1 } { 2 }$ .

A)
B)
C)
D)

Question 29

If the rise of the roof shown in the illustration is 5 feet, and the run is 9 feet, find the pitch of the roof.

A) $- \frac { 5 } { 9 }$
B)45
C) $\frac { 5 } { 9 }$
D)14
E) $\frac { 9 } { 5 }$

Question 30

Find the equation of the line that contains the given point and has the given slope. $( 2,9 ) , m = \frac { 2 } { 9 }$

A) $2 x - 9 y = - 77$
B) $2 x - 9 y = 2$
C) $9 x - 2 y = 2$
D) $2 x - 9 y = - 5$
E) $9 x - 2 y = - 77$

Question 31

Graph the line that passes through the given point and has the given slope. $( 3,2 ) , m = \frac { 5 } { 3 }$

A)
B)
C)
D)
E)

Question 32

Find the distance between the two points. (-4, -2)and (5, 10)

A)15
B)20
C)18
D)12
E)13

Question 33

Find the equation of the line that contains the two given points. Express the equation in the form , where A , B , and C are integers.

Question 34

Find the equation of the line with the given slope and y -intercept. Leave your answer in slope-intercept form.

Question 35

If the ratio of rise to run is to be $\frac { 2 } { 3 }$ for some stairs and the measure of the run is 24 centimeters, find the measure of the rise to the nearest centimeter.

A)36 cm
B)15 cm
C)16 cm
D)26 cm
E)31 cm

Question 36

Find the equation of the line that contains the two given points. $( - 2,0 ) , ( 0 , - 5 )$

A)2 y + 5 x = -10
B)2 y + 5 x = 10
C)2 y - 5 x = -5
D)2 y - 5 x = -10
E)2 y - 5 x = 10

Question 37

Find the equation of the line that contains the given point and has the given slope. $$( - 4,3 ) , m = 0$$

A)x = 3
B)y = 3
C)x = -4
D)y = -4
E)y = -3

Question 38

Find the slope of the line determined by this pair of points. (9, 8), (13, 11)

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

Question 39

Find the distance between the two points. (1, 10)and (9, 2)

A)8
B)16
C) $8 \sqrt { 2 }$
D)9
E) $\sqrt { 16 }$

Question 40

Find the slope of the line determined by this pair of points. (3, -1), (1, -1)slope = __________

Question 41

Graph the line determined by the equation $$y = - \frac { 7 } { 11 } x + \frac { 5 } { 6 }$$ .

A)
B)
C)
D)

Question 42

Find the equation of the line with the given slope and y -intercept. m = 2, b = -7

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

Question 43

Solve $3 x + 2 y = 2$ for y.

A) $2 y = - 3 x + 2$
B) $y = \frac { 3 } { 2 } x + 1$
C) $y = - 2 x + 1$
D) $y = - \frac { 3 } { 2 } x + 1$

Question 44

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

A)

B)

C)

D)

E)

Question 45

Tell whether the lines with the given slopes are parallel, perpendicular, or neither. $m _ { 1 } = 5 , m _ { 2 } = - \frac { 1 } { 5 }$

A)perpendicular
B)parallel
C)neither

Question 46

Determine the type of symmetry exhibited by the graph of the equation. x ² + 4 y = 1

A)symmetry with respect to the x axis
B)symmetry with respect to the y axis
C)symmetry with respect to the origin

Question 47

Use the point-slope form to write an equation of the line with the slope 5 and that passes through the point (7, 9).

A)y + 7 = 5( x - 9)
B)y - 9 = 5( x + 7)
C)y + 9 = 5( x - 7)
D)y - 9 = 5( x - 7)
E)y - 7 = 5( x - 9)

Question 48

Use the point-slope form to write an equation of the line with the slope $- \frac { 3 } { 5 }$ and that passes through the point $( - 9 , - 8 )$ .

A) $y - 9 = - \frac { 3 } { 5 } ( x + 8 )$
B) $y + 9 = - \frac { 3 } { 5 } ( x + 8 )$
C) $y - 8 = - \frac { 3 } { 5 } ( x + 9 )$
D) $y + 8 = - \frac { 3 } { 5 } ( x + 9 )$
E) $y + 8 = \frac { 3 } { 5 } ( x + 9 )$

Question 49

Tell whether the graphs of the following pair of equations are parallel , perpendicular , or neither . $y = 4 x - 14 , y = \frac { 1 } { 4 } x + 27$

A)neither
B)parallel
C)perpendicular

Question 50

Determine the type(s)of symmetry (symmetry with respect to the x axis, y axis, and/or origin)exhibited by the graph the equation. Do not sketch the graph. x ² + y ² - 6 x - 1 = 0

A)y axis
B)x axis
C)origin
D)all three
E)none

Question 51

Graph the equation. $y = - \frac { x ^ { 4 } } { 5 }$

A)
B)
C)
D)
E)

Question 52

Use the point-slope form to write an equation of the line with the slope - 4 and that passes through the point ( -9, 3). Then write your result in slope-intercept form.

A) $y = - 4 x - 32$
B) $y = - 4 x - 31$
C) $y = - 4 x - 33$
D) $y = 4 x - 32$
E) $y = 4 x - 33$

Question 53

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

A)
B)
C)
D)
E)

Question 54

Change the equation to slope-intercept form. $4 x + 11 y = 1$

A) $x = - \frac { 11 } { 4 } y + \frac { 1 } { 11 }$
B) $y = - 4 x + 1$
C) $y = - \frac { 11 } { 4 } + \frac { 1 } { 11 } x$
D) $y = - 4 x + 11$
E) $y = - \frac { 4 } { 11 } x + \frac { 1 } { 11 }$

Question 55

Determine the type(s)of symmetry (symmetry with respect to the x axis, y axis, and/or origin)exhibited by the graph of the equation. Do not sketch the graph. $$x ^ { 2 } + y ^ { 2 } = 19$$

A)origin
B)y axis
C)x axis
D)all three
E)none

Question 56

For the following pair of equations, predict whether they represent parallel lines, perpendicular lines, or lines that intersect but are not perpendicular. 6.7 x + 7.7 y = 4.6 and 7.7 x - 6.7 y = 9.2

A)parallel lines
B)lines that intersect but are not perpendicular
C)perpendicular lines