1. 3.4 – FIND AND USE SLOPES

2. Slope: measures the steepness of a line or the rate of change. Slope = m = Rise Run Up or down Left or right =

3. Type of Slope PictureNumerical Value Positive Negative Any Positive # Any Negative #

4. Type of Slope PictureNumerical Value Zero Undefined 0 Horizontal line Vertical line #. 0

5. 1. Find the slope of the line through the given points. P(3, -5) and Q(1, -1) -4 2 Slope = = Rise Run -4 2 = -2

6. 1. Find the slope of the line through the given points. 4 8 Slope = = Rise Run 4 8 P(5, 2) and Q(-3, -2) = 1 2

7. -6 Slope = = Rise Run Undefined 1. Find the slope of the line through the given points. P(-3, -3) and Q(-3, 3)

8. Slope Formula: Slope = = Rise Run For (x 1, y 1 ) and (x 2, y 2 ) y 2 – y 1 x 2 – x 1

9. 2. Find the slope of the line through the given points using the slope formula. P(-2, -3) and Q(2, -5) (x1,y1)(x1,y1) (x2,y2)(x2,y2) = –5 – (-3) 2 – (-2) = –2 4 =

10. 2. Find the slope of the line through the given points using the slope formula. P(1, -1) and Q(-3, -9) (x1,y1)(x1,y1) (x2,y2)(x2,y2) = –9 – (-1) –3 – 1 = –8 –4 =

11. 2. Find the slope of the line through the given points using the slope formula. P(3, -5) and Q(1, -5) (x1,y1)(x1,y1) (x2,y2)(x2,y2) = –5 – (-5) 1 – 3 = 0 –2 =

12. NameDefinitionSlope Relationship Picture Parallel lines Intersecting lines Lines that never intersect. Same slope Lines that cross at one point Not same m = 2 then m = 2

13. Perp. lines Lines that cross forming right angles Opposite AND reciprocal slopes m = 2 becomes m = – 1212

14. 3. Decide whether the lines are parallel, perpendicular, or neither. neither perpendicular parallel perpendicular

15. 3. Tell whether the lines through the given points are parallel, perpendicular, or neither. Justify your answer. Line 1: (3, 1), (7, 2) Line 2: (-5, -3), (-1, -4) == Line 1: == Line 2: neither

16. 3. Tell whether the lines through the given points are parallel, perpendicular, or neither. Justify your answer. Line 1: (-9, 3), (-6, 7) Line 2: (-11, 5), (-7, 2) == Line 1: == Line 2: perpendicular