1. 4.4 Slope of a Line

2. Slope – a measure of how steep a line is. Slope is the ratio of the vertical change to the horizontal change of a non- vertical line. Section 4.4 Slope of a Line

3. Rise = “The change in Y” Run “The change in x” RISE RUN Rise = 5 Run 7

4. Formula: Slope = rise = y 2 - y 1 run x 2 - x 1 = “The change in Y” “The change in x” (X 2, Y 2 ) (X 1, Y 1 )

5. Positive Slope Negative Slope Horizontal Line = Zero Slope Vertical Line = No Slope or Undefined Slope

6. Examples Find the slope of the order pairs. 1. (4,4),(9,10) Slope = 10-4 = 6 9-45 2. (3,2),(2,3) 3. (-1,4),(3,-2)

7. Answers 2. (3,2),(2,3) 3-2 = 1 = -1 2-3 -1 3. (-1,4),(3,-2) -2-(4) = -6 = -3 3-(-1) 42

8. Parallel Lines – have the same slope These lines are parallel -- The rise/run ratio of both lines is the same

9. Perpendicular Lines – the lines have slopes that are negative reciprocals of each other If this line has a slope of –2/3 ….. Then the slope of any perpendicular line must be 3/2

10. Tell whether the lines are parallel, perpendicular, or neither. Line 1: through (3,2) and (5,7) Line 2: through (0,3) and (-5,5) Find the slope of each line, then compare…. Line 1: slope = 7-2 = 5 5-3 2 Line 2: slope = 5-3 = 2 -5-0-5 -2/5 is the negative reciprocal of 5/2, so these lines are perpendicular.

11. Line 1: Through (-3,1) and (3,4) Line 2: Through (-4,-3) and (4,1) Each line has a slope of ½, so the lines are parallel. Tell whether the lines are parallel, perpendicular, or neither.

12. Homework Text page 230, #20-50 even AND # 51