Envision Math 5th Grade Textbook Answer Key Topic 18.3 Graphing Equations
Graphing Equations
How do you graph an equation on a coordinate grid?
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Each day at 7:00 A.M., Tim listed the temperature on his outdoor thermometer and from the radio weather report.
Question.
Write an equation to show the relationship between the temperatures and then graph that relationship.
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Guided Practice
Do you know HOW?
In 1 and 2, complete the table of values and graph the equation.
Question 1.
y = x+ +3
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Question 2.
y = x – +4
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Do you UNDERSTAND?
Question 3.
For the problem above, suppose the temperature given in the weather report was 2° F higher than the temperature at Tim’s house. Write an equation, make a table of values, and graph the equation.
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Question 4.
On your graph for Problem 1, what is the y-coordinate at the point where the line would cross the x-axis?
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Independent Practice
In 5 through 7, write an equation to describe each table.
Question 5.
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Question 6.
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Question 7.
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In 8 through 10, complete each table of values and graph each equation.
Question 8.
y = x + 1
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Question 9.
y = x – 3
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Question 10.
y = 4 + x
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Write an equation.
Let x = temperature Tim’s house
Let y = temperature given by the weather report
Each day the temperature was reported as 2° lower.
y = x – 2
Use Tim’s list to make a table of values.
A table of values shows how x and y are related and lists values that satisfy the equation.
Use the table of values to graph the equation.
An equation whose graph is a straight line is called a linear equation.
Problem Solving
Question 11.
Reasoning If the points (+1, +7), (+1, +3), (+1, –5), and (+1, –9) were graphed, they would form a vertical line. Do you think the equation for this line would be x = +1 or y = +1? Explain.
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Question 12.
The Clothes Closet was having a year-end sale. Julie bought 2 pairs of jeans. The jeans cost $28 each. Her state charges 7% sales tax. What was the total cost of the jeans?
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Question 13.
Which ordered pair will be included on the graph for y = +9 + x?
A. (+6, +3)
B. (–3, +6)
C. (+3, –6)
D. (+6, –3)
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Question 14.
If you were to walk on Mars, the air near your toes may have a temperature of +18°C, but the air at your head may be 27°C colder. What would be the temperature near your head?
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For 15 and 16, use the graph below.
Question 15.
Make a table of values for the graph.
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Question 16.
Use the table of values to write an equation for the graph.
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Question 17.
Justin bought a hat for $8.50 and socks for $5.75. He had a coupon for $2 off one item. How much change did he receive if he paid with a $20 bill?
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Question 18.
Writing to Explain Aaron’s graph included the points (+6, +2), (+3, –1), and (–3, –7). Bob’s graph included the points (+7, +3), (+2, –2), and (–2, –6). Would all six points be included on the same graph? Why or why not?
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Question 19.
If two pencils cost $0.25, how much would 12 pencils cost?
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