Unit 2: Graphing Equations
Graphing Equations Chapter Test
1. Which line on the graph has a slope of 2/3?
A. Line A
B. Line B
C. Line C
D. Line D
2. Which equation is represented on the graph?
A. y = 4x – 6
B. y = -4x – 6
C. y = 4x +6
D. y = 6x +4
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Unit 2: Graphing Equations
3. Find the slope of the line that has a y-intercept of 3 and contains the point (6,-3).
Patti is tracking the price of gas over a 10 week period. See the graph below to answer questions 4
– 6.
4. What is the y-intercept in this problem? What does it mean in the context of this problem?
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Unit 2: Graphing Equations
5. What is the rate of change between week 3 and week 6?
6. What is the rate of change between week 0 and Week 3? Explain what the rate of change means
in the context of this problem.
7. What is the x intercept for the equation: 3x + 5y = 27?
8. Judy bought 10 shares of a stock on February 1, 2008 for $350. On October 1, 2008 she sold the
stock for $210. Find Judy’s average monthly rate of change on the stock.
9. Graph the following equation on the grid. Identify the slope and the y intercept.
2x +5y = -15
Slope = ___________
Y intercept = ___________
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Unit 2: Graphing Equations
10. Which equation is equivalent to: 4x +2y = -12
A.
B.
y = -2x – 6
y = 2x – 6
11.
C. y = -4x - 12
D. y = -2x + 6
Identify the graph that represents the function: y = |x+3|
A.
B.
C.
D.
12. Joe is traveling to his sister’s house for Thanksgiving. He begins his drive at 3am. He drives
210 miles in 3 hours. He then stops for a half hour break and drives another 90 miles in the
next 2 hours. His trip ends at 10 am after driving a total of 377.5 miles.
•
•
•
Create a graph to illustrate this problem.
What is Joe’s average rate of change between 3 am and 6 am?
If Joe’s rate of change for the first three hours had remained constant throughout the entire
trip, what time would he have arrived at his sister’s house?
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Unit 2: Graphing Equations
13. A final exam contains multiple choice questions that are worth 2 points and free response
questions that are worth 3 points. The test is worth 60 points. The equation that represents x
multiple choice questions and y free response questions is:
2x +3y = 60.
• Graph the equation on the grid. Let x = the number of multiple choice questions and
y = the number of free response questions.
•
If there are 15 multiple choice questions on the test, how many free response questions are
on the test? Justify your answer.
•
Identify one other possibility for the number of each question on the test: Justify your
answer.
There could be _______ multiple choice and _______ free response.
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Unit 2: Graphing Equations
Graphing Equations Chapter Test – Answer Key
1. Which line on the graph has a slope of 2/3? (1 Point)
A.
A Line A
B. Line B
C. Line C
D. Line D
**Note: You can eliminate C & D
immediately because they have negative
slopes.
Then you only need to count the slope for A
& B.
2. Which equation is represented on the graph?
(1 Point)
A.
A y = 4x – 6
.
B. y = -4x – 6
C. y = 4x +6
D. y = 6x +4
**This is another problem where you can
eliminate answers that don’t make sense. You
know the y – intercept is -6, so C & D can be
eliminated!
The line is rising so the slope is positive.
Therefore, B can also be eliminated!
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Unit 2: Graphing Equations
3. Find the slope of the line that has a y-intercept of 3 and contains the point (6,-3). (2 points)
Slope = rise
run
from one point to the next
Slope = 1 = -1
-1
Patti is tracking the price of gas over a 10 week period. See the graph below to answer questions 4
– 6.
4. What is the y-intercept in this problem? What does it mean in the context of this problem?
(2 points)
The y-intercept is 2.40. In this problem the y-intercept indicates that when Patti first began tracking
gas prices (week 0), the price was $2.40.
5. What is the rate of change between week 3 and week 6? (2 Points)
Ordered pairs: (3, 3.20) (6, 2.20)
y2 – y1 = 2.20 – 3.20 = -1
The rate of change between week 3 and 6 is -1/3. This means
x2 – x1
6–3
3
that the price of gas dropped about $0.33 each week.
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Unit 2: Graphing Equations
6. What is the rate of change between week 0 and Week 3? Explain what the rate of change means
in the context of this problem. (3 Points)
Ordered pairs: (0, 2.40) (3, 3.20)
y2 – y1 = 3.20 – 2.40= .8 = .27
x2 – x1
3–0
3
The rate of change between week 0 and 3 is .27. This means
that the price of gas rose about $0.27 each week between
weeks 0 and 3.
7. What is the x intercept for the equation: 3x + 5y = 27? (2 points)
X intercept: Let y = 0
3x +5(0) = 27
3x = 27
3x = 27
3
3
x=9
The x intercept is 9.
8. Judy bought 10 shares of a stock on February 1, 2008 for $350. On October 1, 2008 she sold the
stock for $210. Find Judy’s average monthly rate of change on the stock. (2 points)
Ordered pairs: (2, 350)
(10, 210)
y2 – y1 = 210 – 350 = -140 = -17.5
x2 – x1
10-2
8
Feb is month 2
October is month 10
Judy’s average monthly rate of change is -17.5.
She lost 17.5 dollars per month while holding
that stock.
9. Graph the following equation on the grid. Identify the slope and the y intercept. (3 points)
2x +5y = -15
I am going to rewrite it in slope
intercept form:
Slope = -2/5
2x -2x +5y = -15 – 2x
Y intercept = -3
5y = -2x – 15
5y = -2x – 15
5
5 5
y = -2/5x -3
10. Which equation is equivalent to: 4x +2y = -12 (1 point)
4x – 4x +2y = -12 – 4x
2y = -4x – 12
A.
B.
y = -2x – 6
y = 2x – 6
C. y = -4x - 12
D. y = -2x + 6
2y = -4x – 12
2
2
2
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y = -2x -6
Unit 2: Graphing Equations
11.
A.
Identify the graph that represents the function: y = |x+3|
B.
C.
(1 point)
D.
You can eliminate answer B because it represents a negative absolute value, since it is upside
down. We also know that the graph shifts up if there is a constant after the absolute value.
Therefore, we’ve narrowed it down to A or D. Since y = 0, which x value would make sense, -3 or
3? -3 + 3 = 0, so the correct answer is A.
You can also make a table of value and see which graph has the same points as the table of
values.
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Unit 2: Graphing Equations
12. Joe is traveling to his sister’s house for Thanksgiving. He begins his drive at 3am. He drives
210 miles in 3 hours. He then stops for a half hour break and drives another 90 miles in the
next 2 hours. His trip ends at 10 am after driving a total of 377.5 miles.
(4 points)
•
•
•
Create a graph to illustrate this problem. (2/4 points)
What is Joe’s average rate of change between 3 am and 6 am?
If Joe’s rate of change for the first three hours had remained constant throughout the entire
trip, what time would he have arrived at his sister’s house?
Rate of change = slope
Two points: 3am (3, 0)
6am (6, 210)
Slope = y2 – y1 = 210-0 = 210 = 70
X2 – x1
6–3
3
The rate of change between 3am and 6 am is 70. Therefore, Joe maintained a constant rate
of 70 miles per hour during this three hour time period.
If Joe had been able to maintain a constant rate of 70 miles per hour throughout his entire trip he would have arrived
at his sister’s house at 8:24 am.
D= rt
377.5 = 70t
Distance = 377.5 miles
Rate = 70 miles per hour
Time = ?
377.5 = 70t
70
70
T = 5.4 (5 hours and 24 minutes) ** .4 = 4/10 = 2/5. 2/5 of 60 minutes = 2/5 •60 = 24
3 am plus 5 hours and 24 minutes = 8:24 am.
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Unit 2: Graphing Equations
12. A final exam contains multiple choice questions that are worth 2 points and free response
questions that are worth 3 points. The test is worth 60 points. The equation that represents x
multiple choice questions and y free response questions is:
2x +3y = 60. (4 points)
• Graph the equation on the grid. Let x = the number of multiple choice questions and
y = the number of free response questions.
In order to graph the equation, we must find
the x and y intercepts:
2x +3y = 60
X Intercept
Y Intercept
2x +3(0) = 60
2(0) +3y = 60
2x = 60
2
2
3y = 60
3
3
x = 30
X intercept = 30
•
y = 20
Y intercept = 20
If there are 15 multiple choice questions on the test, how many free response questions are
on the test? Justify your answer.
Since•we know there are 15 multiple choice questions, we can substitute 15 for x and solve for y.
2(15) + 3y = 60
30+3y = 60
30 – 30 +3y = 60 – 30
3y = 30
3y/3 = 30/3
Y= 10
•
If there are 15 multiple choice questions, then there are 10 free
response questions.
Justify: 2(15) + 3(10) = 60
30+30 = 60
Identify one other possibility for the number of each question on the test: Justify your
answer.
There could be _______ multiple choice and _______ free response.
There could be 21 multiple choice and 6 free response.
2(21) + 3(6) = 60
42 + 18 = 60
60 = 60
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This test is worth 28 points