Understanding slope and y-intercept Student Activity Sheet 2; use with Exploring Connecting rate of change and slope

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Elinor Young
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1 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. Page 1 of 8

2 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. Page 2 of 8

3 6. REINFORCE Create a sketch of stair steps with steepness corresponding to a slope of a. Complete the process column of the table. Skater s Distance from Motion Detector Elapsed time in seconds Process Distance in feet Page 3 of 8

4 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 Page 4 of 8

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?

5 Use the graph below for questions 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 y, distance from motion detector Page 5 of 8

6 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. Page 6 of 8

7 Match the graphs to the corresponding situations described in questions Write the letter of the graph in the space next to the situation it matches. A B C D E Michael begins with $25, and spends $1 each week. Tara gains 1 friend each week. Mira runs to the mailbox, moving away from the house. José slowly jogs toward the finish line. He stops to rest before he gets to the finish line. Margaret just stands and watches the sunset. 21. REINFORCE Determine the slope of the line that connects the points (10,2) and (4,8). Page 7 of 8

8 22. REINFORCE Sketch a line passing through the point (1,3) with a slope of 2. Page 8 of 8

The Picture Tells the Linear Story

The Picture Tells the Linear Story Students investigate the relationship between constants and coefficients in a linear equation and the resulting slopes and y-intercepts on the graphs. This activity also