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6th Grade Pre-Algebra Chapter 8
Name:
Date: ______ Block: ______
Vocabulary
Write the definition of each term in your own words then write an
appropriate example.
1) Relation:
__________________________________________________________________
2) Domain:
__________________________________________________________________
3) Range:
__________________________________________________________________
4) Function:
__________________________________________________________________
5) x-intercept:
__________________________________________________________________
6) y-intercept:
__________________________________________________________________
7) Slope:
____
__________________________________________________________________
8) Slope intercept form:
__________________________________________________________________
9) Standard form:
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10) Function notation:
__________________________________________________________________
11) Linear Equation: ______________________________________________________
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12) Solution of linear equations _____________________________________________
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Skills
13) Identify the domain and range of the relation. (5, 2), (−1, 3), (3, −2), (−1, 3), (−4, 5)
Domain: _______________________
Range: ______________________________
Represent the relation as a graph and as a mapping diagram. Then tell whether the
relation is a function. Explain your reasoning.
14) (8, −5), (−6, 3), (5, 3), (8, −8), (4, 0)
Function
y
Not a function
Explain:
x
Tell whether the relation represented by the graph is a function.
y
Function
15)
Not a function
x
Explain:
_____
Tell whether the ordered pair is a solution of
−𝟐𝒙 + 𝒚 = 𝟖.
16) (−2, 4)
17) (2, −4)
__________
__________
18) Let f(x) = 3x – 2
1
19) Let f(x) = - 4x + 3
Find f(x) when x = -1
Find x when f(x) = 1
y
Graph the linear equations.
20) 𝑦 = −3𝑥 + 4
(𝑥, 𝑦)
𝑥
x
y
1
21) 𝑦 = 4 𝑥 − 6
x
Find the x and y intercepts of each equation then graph the equations.
22) 2𝑥 − 6𝑦 = 12
23) −𝑥 + 4𝑦 = 8
y
y
x
x
Find the slope of the line through the given points.
24) (2, –5), (6, 1)
25) (0, –3 )( 4, –7)
y
y
x
x
26)
27)
Identify the slope and the y-intercept of the line with the given equations then graph
each.
y
y
2
28) 𝑦 = − 5 𝑥 + 8
29) 𝑦 = 4𝑥 − 6
x
x
y
y
30) 3𝑥 + 𝑦 = 7
31) −2𝑥 − 4𝑦 = 12
x
x
y
y
32) 𝑥 = 3
33) 𝑦 = −6
x
x
Find the slope of a line parallel to the given line and the slope of a line perpendicular to the given line.
34)
35) 𝑦 = 2𝑥 − 6
Slope:
_______
Slope:
Parallel:
_______
Parallel:
Perpendicular: _______
36) 3𝑥 + 6𝑦 = 18
_______
Slope: _______
_______
Parallel: _______
Perpendicular: _______
Perpendicular: _______
Write an equation of the line with the given information.
37)
1
38)
slope = − 2 y − intercept = 3
slope = 5 y − intercept = −8
Write an equation in slope-intercept form that goes through the 2 given points.
39)
40)
_______________________
_______________________
(3, 6) (0, 3)
41)
(−1, −8) (0, 9)
_______________________
Write an equation of the line that is parallel to the linear equation and goes through the
given point.
−2
42) 𝑦 = 4𝑥 + 3 ; (0, −6)
43) 𝑦 = 𝑥 − 2 ; (0, 3)
3
_______________________
_______________________
Write an equation of the line that is perpendicular to the linear equation and goes through
the given point:
44)
𝑦 = 3𝑥 + 5 ; (0, −7)
_______________________
45)
𝑦=
−4
5
𝑥 − 4 ; (0, 2)
_______________________
46) Tell whether (-1, 3) is a solution of the linear system: y = 5x -2 and y = -2x + 5.
47) Solve the linear system by graphing: 2x – 3y = 12 and x – y = 3
y
x
Applications
48) Suppose that after a volcanic eruption, lava from the volcano traveled 12 miles to a body
of water at an average speed of 3 miles per hour. Write an equation to show the lava's
distance 𝑦 (in miles) from the water 𝑥 hours after it left the volcano.
a.) Make a table of solutions for the equation.
𝑥
(𝑥, 𝑦)
b.) How long did it take the lava reach the water?
c.) Explain what the ordered pair (2, 6) means.
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__________________________________________________________________________________________
You are in charge of buying food for a party. You have budgeted $54.00 for pizza and
soda. A pack of soda costs $6.00 and one pizza costs $3.00.
a)
Write an equation describing the possible amounts of pizza and soda you can buy.
b)
Use intercepts to graph the equation.
y
18
16
14
Pizzas
49)
12
10
8
6
c)
If you buy 2 pizzas, how many packs of soda can you buy?
4
2
2
4
6
8
10
12
14
16
Packs of soda
18
x
Writing
Answer the following questions in complete sentences. Be sure to use examples
and correct math terminology when possible.
50) Explain how to find the whether a point is a solution to a linear equation.
51) Describe 2 different strategies to graph a linear equation.