SLOPE How did we define slope yesterday When

SLOPE!!! • How did we define slope yesterday? • When looking at a graph to determine if the slope is positive, negative, zero, or undefined what direction should we look? • I want to find the “rise over run” of a line what should I find first on the line? • Explain what we mean by “rise” and “run”. • How might we encounter slope in the real world? M. Pickens 2006

What is Slope? Slope is the rate of change of a line (change in y) (change in x) M. Pickens 2006

Slope Line Review • If a line rises from left to right, its slope is _______. • If a line falls from left to right, its slope is _______. • A horizontal line has a _____ slope. • A vertical line has a _______ slope. M. Pickens 2006

What does the line look like when… • You have positive slope? • You have negative slope? • You have zero slope? • You have NO slope? M. Pickens 2006

Positive slope, + work Negative slope, - work Zero slope is zero fun! NO slope. Oh No!!!! Slope Mountain Ski Resort M. T. Pickens Merrill 2005 2006

What Type of Slope is Shown? Positive Slope Negative Slope Zero Slope No Slope/Undefined M. Pickens 2006

Review Slope of a Graph • Identify 2 points on a line. • Find the rise and run. • Determine if the slope is positive or negative. How far up or down it changes How far left or right it changes M. Pickens 2006

Slope M. Pickens 2006

Slope of a Graphed Line Find the slope of each line below y Slopes: Find the slope of each line below x 4 4 M. Pickens 2006

Objectives • To learn what slope is • To learn what a line looks like when it has positive, negative, zero or undefined slope • To learn how to find the slope of a graph • To learn how to find the slope given 2 points • To learn how to find the slope of a table M. Pickens 2006

Slope of line through 2 points • To find the slope of a line through 2 given points we use the formula • For example, Find the slope of a line 18 that goes through (-3, -3 55) and (2, 2 18) X 1 y 1 X 2 y 2 M. Pickens 2006

Given two points on a line, find the slope: 1. (9, 2), (8, -7) X 1 y 1 X 2 y 2 2. (-4, 4), (-7, 2) X 1 y 1 X 2 y 2 3. (5, -1), (9, -4) X 1 y 1 X 2 y 2 M. Pickens 2006

Given two points on a line, find the slope: 4. (5, 2), (1, 0) X 1 y 1 X 2 y 2 5. (3, -3), (3, -1) X 1 y 1 X 2 y 2 Undefined, NO slope 6. (-4, -2), (4, -2) X 1 y 1 X 2 y 2 M. Pickens 2006

Slope of a Table • In a table we can use the same formula. Pick any two pairs in the table for coordinates x 1 x 2 x -4 1 3 8 10 y -17 -2 4 19 25 Pick any two rows. If it is linear it will be the same no matter which two rows you pick y 1 y 2 M. Pickens 2006

Slope of a Table • Find the slope for each table below x -3 -1 0 1 5 y 4. 25 2. 75 2 1. 25 -1. 75 x -8 -6 -3 -1 0 y 2 3 4. 5 5. 5 6 M. Pickens 2006

Slope of a Table • Find the slope for each table below x -10 -5 -1 5 10 y 17 10 4. 4 -4 -11 x -3 -1 0 1 4 y -8 -8 -8 M. Pickens 2006

Conclusion • Slope is: the rate of change of a line • Describe the slope of each of the following Negative slope Undefined/ No slope Positive slope Zero/0 slope M. Pickens 2006