1. Linear Functions 6.1 SLOPE OF A LINE

2. Today’s Objectives Demonstrate an understanding of slope with respect to: rise and run; rate of change; and line segments and lines, including: Determine the slope of a line or line segment using rise and run Classify a line as having either positive or negative slope Explain the slope of a horizontal or vertical line Explain why the slope can be found using any two points on the graph of the line or line Draw a line segment given its slope and a point on the line

3. Slope of a Line

4. A)Counting B)Slope formula A (-2,1) B(4,-2) Down 3 Right 6 Slope = rise/run Slope = -3/6 Slope = -1/2 (x 1,y 1 ) (x 2,y 2 ) Slope = rise/run = y 2 -y 1 /x 2 -x 1 Slope = [-2-1]/[4-(-2)] Slope = -3/6 = -1/2

5. Slope of a Line If the line segment goes downward from left to right, it will have a negative slope. (rise = negative) If the line segment goes upwards from left to right, it will have a positive slope. (rise = positive) *The steeper the line goes up or down, the greater the slope.

6. Horizontal and Vertical Lines

7. Example Find the slopes of the following line segments. Which line segment has the steepest slope? Graph the line segments. A) A(-1, 7)B(4, -3) B) A(-20, 3)B(-4, -5)

8. Solutions Slope of line a) = -10/5 = -2Slope of line b) = -8/16 = -1/2 Line segment in a) is steeper than line segment b) (-20,3) (-4,-5) (-1,7) (4,-3)

10. Example) Determine the slope of the following graph: Known point (5, -6) (12, -8) (-2, -4) y 2 – y 1 = -8 – (-6) = -2 = -0.29 x 2 – x 1 12 – (-5) 7

11. Example) Anna has a part time job. She recorded the hours she worked and her pay for three different days. Use the table to draw a graph that represents the data. Slope: 12 The slope represents Anna’s hourly rate of pay. Anna earned $42 in 3.5 hours. It took Anna 2.5 hours to earn $30. Time (h)Pay ($) 00 224 448 672