1. The Slope of a Line 4.4 Objective 1 – Find the slope of a line using two of its points Objective 2 – Interpret slope as a rate of change in real-life situations

2. ( x 2, y 2 ) ( x 1, y 1 ) Finding the Slope of a Line ( y 2 - y 1 ) ( x 2 - x 1 ) x y (rise) (run) The slope m of the non-vertical line passing through the points (x 1, y 1 ) and (x 2, y 2 ) is: m = rise change in y y 2 - y 1 run change in x x 2 - x 1 ==

3. EXAMPLE 1 A line with a positive slope rises Find the slope of the line passing through (-2, 2) and (3, 4) x y (-2, 2) (3, 4) 2 5 Let (x 1, y 1 ) = (-2, 2) and (x 2, y 2 ) = (3, 4) m = y 2 – y 1 x 2 – x 1 slope = Rise Run m = 4 – 2 3 - (-2) m = 2 3 + 2 m = 2 5 Substitute values Simplify Slope is positive Positive slope: line rises from left to right.

4. y x y EXAMPLE 2 A line with a negative slope falls Find the slope of the line passing through (0, 0) and (3, -3) Let (x 1, y 1 ) = (0, 0) and (x 2, y 2 ) = (3, -3) m = y 2 – y 1 x 2 – x 1 slope = m = -3 – 0 3 - 0 Substitute values m = -3 3 Simplify m = Slope is negative Negative slope: line falls from left to right. (0, 0) (3, -3) -3 3

5. EXAMPLE 3 A line with zero slope is horizontal x y Find the slope of the line passing through (-1, 2) and (3, 2) Let (x 1, y 1 ) = (-1, 2) and (x 2, y 2 ) = (3, 2) m = y 2 – y 1 x 2 – x 1 slope = m = 2 – 2 3 – (-1) Substitute values m = 0 4 Simplify m = 0 Slope is zero Zero slope: line is horizontal. (-1, 2) (3, 2)

6. x y EXAMPLE 4 The slope of a vertical line is undefined Find the slope of the line passing through (2, 4) and (2, 1) m = y 2 – y 1 x 2 – x 1 slope = m = 1 – 4 2 – 2 Substitute values m = -3 0 Division by 0 is undefined (2, 4) (2, 1) Undefined slope: line is vertical. No Slope

7. On your own Find the slope of the lines that pass through the following points. 1) (2, 7) (-3, 8) 2) (-5, 2) (6, 3) 3) (6, -4) (-2, -4) 8 – 7 -3 – 2 1 –5 3 – 2 6 – (– 5) 1 11 -4 – (-4) -2 – 6 0 -8 Zero slope