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Date:
Period:
Algebra 1
Unit 3 Exam Review
Study Guide:
y=x
y= - 3x
y=7x
y= - 2x
y=1/2x
y= - 1/5x
The larger the slope the steeper the line.
** Ignoring the sign of the slope **
The smaller the slope the less steep/ flatter the line.
** Ignoring the sign of the slope **
y= 2x
y=-2x
f(x)=2x + 5
g(x)=2x - 3
The y-intercept moves the graph up or down. Function g(x) is 8 units below f(x).
Parent Linear Function y=x
Domain: all real numbers
Range: all real numbers
Formulas:
Given that (𝑥1 , 𝑦1 ) and (𝑥2 , 𝑦2 ) are points on a line
Slope-Intercept Form: 𝑦 = 𝑚𝑥 + 𝑏
Slope: 𝑚 =
𝑦2 −𝑦1
𝑥2 −𝑥1
Point-Slope Form: 𝑦 − 𝑦1 = 𝑚(𝑥 − 𝑥1 )
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Date:
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1) Jenny tracks the amount of money raised for the school fund-raiser in the table below.
What is the constant of variation?
2) If y varies directly with x, and y is 84 when x is 16, which of the following represents this situation?
A
y = 100x
B
y = 68x
C
y=
21
x
4
D
y=
3) Consider the following graph of the equation y=3x + 4
and answer the questions below.
a) What would the graph look like
if you decrease the slope by 2?
b) What would the graph look like
if you increase the y-intercept by 2?
4
x
21
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4) The function y = −3x − 8 is graphed below.
In the function above, the slope will be multiplied by −2, and the y-value of the y-intercept will be
increased by 2 units.
Which of the following graphs best represents the new function?
F
G
H
J
5) Which linear function includes the points (–3, 1) and (–2, 4)?
1
x+2
3
F
f(x) = 3x + 10
G
f(x) =
H
f(x) = 3x – 6
J
f(x) = −3x + 1
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6) The graph of the line containing the points (-6, -5) and (3,1) is shown below.
If the slope of this line is multiplied by -3 and the y-intercept remains the same, which of the following
best represents the graph of the resulting line?
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Date:
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7) Kirk repairs computers. He charges an hourly rate plus a base fee for his services. The table below
shows the relationship between h, the number of hours of labor, and c, the total cost for Kirk’s
services. If Kirk decides to keep his base fee the same but increase his hourly rate by $2, what will be
the total cost for 8 hours of work?
A
B
C
D
$112
$141
$143
$157
8) Graph the following equation using x and y intercepts.
5x – 4y = 40
9) Determine the x-intercept and y-intercept from the graph below. Explain what each means.
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10) Which best describes the effect on the graph of f (x) = 4x + 8 if the y-intercept is changed to −3?
11) Graph a line through the given point, with the given slope.
a) (3, -2); slope = -6
b) (-4, 7); slope =
5
2
12) Write an equation of a line with the given slope and y-intercept and graph each line.
m=-
2
,b=6
4
Equation: _______________
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Date:
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13) Are the following direct variation? If yes, what is the constant of variation?
a) y = 3x + 5
b) y = 2x
c) y = -
3
x
4
.
14)Circle the graphs that are direct variation.
15) Direct variation equations all pass through the __________.
16) Determine the equation of the line given the slope and y-intercept.
4
; y-intercept is 1
5
a) Slope = 6; y-intercept is 7
b)Slope =
Equation: ________________
Equation: __________________
c) Slope =
5
; y-intercept is -2
3
Equation: _______________
d) Slope = -8; y-intercept is -10
Equation: __________________
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Date:
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17) Write an equation of a line with the given slope and y-intercept and graph each line.
2
,b=2
4
a) m = 6, b = -4
b) m = -
Equation: _______________
Equation: ________________
For questions 18-23, graph each equation.
18) y =
1
x–4
3
21) 2x + 5y = -20
19) y =
7
x+3
2
22) y – x = 2
20) y = 2
23) 4x = 2y – 8
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24) Write the equation of each graph below.
a)
b)
Equation: ________________
Equation: __________________
25) Determine the equation of the line given a point and slope. Put your answer in slope-intercept
form. Use point-slope formula.
(5, -3); m = 2
Equation: __________________
For questions 26-29, write the equation of the line in slope-intercept form.
26) (4, 8), (2, 12)
27) (8, -2), (14, 1)
Equation: _______________
Equation: __________________
28) (-5, 13), (-10, 9)
29) (11, 7), (9, 3)
Equation: _______________
Equation: __________________