Student:
Class:
Date:
Understanding slope and y-intercept
Student Activity Sheet 2; use with Exploring “Connecting rate of change and slope”
1. The y-value of the point at which a graph crosses the y-axis is called the _________.
2. _____is a measure of the steepness of a line.
3. Calculate the rate of change by analyzing the differences in the y-values and the
differences in the x-values.
Copyright 2014 Agile Mind, Inc. ®
Content copyright 2014 Charles A. Dana
Center, The University of Texas at Austin
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Student:
Class:
Date:
Understanding slope and y-intercept
Student Activity Sheet 2; use with Exploring “Connecting rate of change and slope”
4. REINFORCE Suppose you leave your house and ride your bike to the mall at a steady rate.
You hang out with some friends for a while, and then you realize you have stayed too long
and must hurry home. You ride home at a steady rate, but faster than the rate at which
you rode to the mall. Sketch a graph that represents this situation.
5. REINFORCE Describe a situation that could be represented by this graph.
Copyright 2014 Agile Mind, Inc. ®
Content copyright 2014 Charles A. Dana
Center, The University of Texas at Austin
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Student:
Class:
Date:
Understanding slope and y-intercept
Student Activity Sheet 2; use with Exploring “Connecting rate of change and slope”
6. REINFORCE Create a sketch of stair steps with steepness corresponding to a slope of
2
.
3
7.
a. Complete the process column of the table.
Skater’s Distance from Motion Detector
Elapsed time in seconds
Process
0
1
2
3
4
5
6
7
8
9
10
Copyright 2014 Agile Mind, Inc. ®
Content copyright 2014 Charles A. Dana
Center, The University of Texas at Austin
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Distance in feet
0.7
1.1
1.5
1.9
2.3
2.7
3.1
3.5
3.9
4.3
4.7
Student:
Class:
Date:
Understanding slope and y-intercept
Student Activity Sheet 2; use with Exploring “Connecting rate of change and slope”
b. Can you write a function rule that expresses the relationship between the elapsed
time, x, and the distance from motion detector, y?
c. How are the slope and y-intercept of the graph of the data represented in your rule?
8. What is slope-intercept form?
9. Identify the slope, m, and the y-intercept, b, of the equation y = 0.4x + 0.7.
Copyright 2014 Agile Mind, Inc. ®
Content copyright 2014 Charles A. Dana
Center, The University of Texas at Austin
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Student:
Class:
Date:
Understanding slope and y-intercept
Student Activity Sheet 2; use with Exploring “Connecting rate of change and slope”
Use the graph below for questions 10-11.
10. Is the distance from the motion detector increasing or decreasing?
11. What are the y-intercept and slope of the graph? Explain both in terms of the
skateboarding context.
x, time in seconds
0
1
2
3
4
5
6
7
8
9
10
Copyright 2014 Agile Mind, Inc. ®
Content copyright 2014 Charles A. Dana
Center, The University of Texas at Austin
y, distance from motion detector
7
6.4
5.8
5.2
4.6
4
3.4
2.8
2.2
1.6
1
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Student:
Class:
Date:
Understanding slope and y-intercept
Student Activity Sheet 2; use with Exploring “Connecting rate of change and slope”
12. Use the slope and the y-intercept you found in question 11 to write an equation. To verify
your equation, check the function for at least one input value.
You have learned about the connections between a constant rate of change, the slope of a
line, and a linear function. Can you solve this puzzle to check your understanding of these
important concepts?
rate of change constant slope linear function
13. When talking about how quickly or slowly a linear function is changing, you are discussing
the function’s ____________.
14. The graph of a ____________ forms a straight line. The line is straight because the
linear function has a _________ rate of change.
15. When you graph a linear function, __________ refers to the steepness of the line the
function makes. The slope of this line is the same as the _________ of the linear
function. The slope can be expressed as a decimal, fraction, or integer.
Copyright 2014 Agile Mind, Inc. ®
Content copyright 2014 Charles A. Dana
Center, The University of Texas at Austin
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Student:
Class:
Date:
Understanding slope and y-intercept
Student Activity Sheet 2; use with Exploring “Connecting rate of change and slope”
Match the graphs to the corresponding situations described in questions 16-20. Write the
letter of the graph in the space next to the situation it matches.
A
B
C
D
E
16.
Michael begins with $25, and spends $1 each week.
17.
Tara gains 1 friend each week.
18.
Mira runs to the mailbox, moving away from the house.
19.
José slowly jogs toward the finish line. He stops to rest before he gets to the finish line.
20.
Margaret just stands and watches the sunset.
21. REINFORCE Determine the slope of the line that connects the points (10,2) and (4,8).
Copyright 2014 Agile Mind, Inc. ®
Content copyright 2014 Charles A. Dana
Center, The University of Texas at Austin
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Student:
Class:
Date:
Understanding slope and y-intercept
Student Activity Sheet 2; use with Exploring “Connecting rate of change and slope”
22. REINFORCE Sketch a line passing through the point (1,3) with a slope of 2.
Copyright 2014 Agile Mind, Inc. ®
Content copyright 2014 Charles A. Dana
Center, The University of Texas at Austin
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