7.5.5 Slope

Vocabulary Slope: The rate of change between two points on a line. It measures how steep a line is, at what rate its climbing TIP: The slope of a line is the SAME between ANY two points on that line because the rate of change is always the same Slope Formula = Change in Y Change in X Slope is also referred to “rise over run” Rise Run X value is also referred to as Input (the way IN to a graph Y value is also referred to as OUTput (the way OUT of a graph)

Slope In Action You’re saving up to buy a new computer. Your parents have promised you that for every $1 you save, they will contribute $2 to your computer money. On the first week (because you’re so excited), you work hard at odd jobs and are able to save $25!! So your parents give you $50 to put in the jar where you’re stashing the cash. On the next week (when your enthusiasm has faded a little) you’re only able to save $8 so your parents give you $16. Change in Y = 16 – 50 = -34 -34 = 2 Change in X = 8 – 25 = -17 -17 1 If this “line” continues, your slope will always be 2 1 $2 from your parents for every $1 you put in.

Why Rise Over Run? Why do we put in the change in Y on top of the slope formula? If the x value is the way “in” to a graph, shouldn’t it go on top of the slope formula? Well, think about the computer you’re saving up for. You’re putting IN (remember INput = x value) one dollar to get OUT (remember OUTput = y value) $2 from your parents. Last I checked, 2 is far different from 1 1 2 The first slope would look like this: The second slope, well… Which hill increases in height faster, huh? Which slope will get you money faster?

Slope Test, Cont’d Let’s say your family has a “Remember to be Kind” jar in the kitchen. Your parents decided to put it there because you and your siblings have been fighting recently. Your parents have told all of you, for every mean thing you do to each other, you need to put $2 in the “Kind” jar. If this were to be represented on a line, it would always be (1, -2) as in, 1 mean thing will result in a loss of $2 from you. If you wanted to draw a line for the “Kind” jar, it would be (1, 2) as in, 1 mean thing will result in an addition of $2 to the jar. As long as the rate stays the same, the slope (the line) will always be the same at any two points on the line. If you do 5 mean things (wow!!!) that is a loss of $10 for you!

Find the Slope 0 - 4 = -4 0 - 3 = -3 Slope = 4 3 Slope = Change in Y Change in X (or, the change in RISE over the change in RUN) 0 - 4 = -4 0 - 3 = -3 Slope = 4 3

Find the Slope

Graph The Data & Find The Slope Gallons, x 5 10 15 20 Miles, y 162.5 325 487.5 650

Graph The Data

Find the Slope Gallons, x 5 10 15 20 Miles, y 162.5 325 487.5 650 Change in Y = 162.5 Change in X = 5 Slope = 162.5 5

Camping Trip The graph on the next page shows the amount of money you and a friend are saving for a camping trip. a. Compare the steepness of the lines. What does this tell you about the rate of saving between you and your friend? b. Find the slope of each line c. How much more money does your friend save each week than you? d. The camping trip costs $165. How long will it take you to save enough money?

Homework Page 196 (# 2, 3, 4, 5, 6, 7, 10, 12, 17, 19)