1. Algebra 4.4 Slope

2. Finding Slope m = slope = rise run = change in y change in x y 2 – y 1 = x 2 – x 1 x y.. (x 1, y 1 ) (x 2, y 2 ) The order the arcs subtract does not matter, as long as the order is the same for both!

3. Find the slope of the line. 4 – 2 = 3 – (-2) x y.. (-2, 2) (3, 4) y 2 – y 1 = x 2 – x 1 slope 2 = 3 + 2 2 = 5 The slope of the line is 2/5.

4. You try! Find the slope of the line. 1 – (-5) = -2 – 1 x y.. (-2, 1) (1, -5) y 2 – y 1 = x 2 – x 1 slope 1 + 5 = -3 = The slope of the line is -2. 6 Can you simplify slope? Yes!

5. Try another. Find the slope of the line. 2 – 2 = 3 – (-1) x y.. (-1, 2)(3, 2) y 2 – y 1 = x 2 – x 1 slope 0 = 3 + 1 = 4 The slope of the line is 0. 0 All horizontal lines have a zero slope. It’s like jogging on flat ground, your slope is zero.

6. How about the slope between (2, 1) and (2, 4)? 4 – 1 = 2 - 2 y 2 – y 1 = x 2 – x 1 slope 3 = 0 The slope of the line is undefined. All vertical lines have an undefined slope. It’s like going up in an elevator, your rise can be anything, but your run is zero. x y.. (2, 1) (2, 4)

7. Every type of slope. Positive Slope Greater than 1 Uphill Steep Positive Slope Less than 1 Uphill Flatter Negative Slope Greater than 1 Downhill Steep Negative Slope Less than 1 Downhill Flatter Slope = 0 Undefined Slope Running up the hill is undefined!

8. Identifying a Slope of -3. Is it uphill or downhill? Downhill Is it steep or flatter? Steep Rise -3 Run 1

9. Identifying a Slope of 1/4. Is it uphill or downhill? Uphill Is it steep or flatter? Flatter Rise 1 Run 4

10. Identifying a Slope of -2/3. Is it uphill or downhill? Downhill Is it steep or flatter? Flatter Rise -2 Run 3

11. Find the value of y so that the line passing through the points (-2, 1) and (4, y) and has a slope of 2/3. y – 1 = 4 – (-2) y 2 – y 1 = x 2 – x 1 slope y - 1 = 6 = 3 2 3 2 Clear the fraction by multiplying by the LCD 6 6 4 = y 5

12. Find the value of y so that the line passing through the points (3, y) and (5, 8) and has a slope of 2. 8 – y = 5 – 3 y 2 – y 1 = x 2 – x 1 slope 8 - y = 2 = 2 2 Multiply each side by 2. 2 2 4 = - y -4 = y 4

13. Homework P. 230 #13 -19 Odd (graph, no graph paper required) # 21 - 41 Odd (calculate, do not graph)