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Section 2.3 Rate of Change & Slope of a Line

Section 2.3 Rate of Change & Slope of a Line. Average Rate of Change Slope of a Line Applications Horizontal & Vertical Lines Slopes of Parallel Line Slopes of Perpendicular Lines. Slope is a Ratio: Average Rate of Change Examples. What is Slope & Why is it Important?.

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Section 2.3 Rate of Change & Slope of a Line

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  1. Section 2.3Rate of Change & Slope of a Line • Average Rate of Change • Slope of a Line • Applications • Horizontal & Vertical Lines • Slopes of Parallel Line • Slopes of Perpendicular Lines

  2. Slope is a Ratio:Average Rate of Change Examples

  3. What is Slope & Why is it Important? • Using any 2 points on a straight line will compute to the same slope. • We use the letter m to stand for a line’s slope

  4. Examples • Compute the slope of a line passing through (-2,4) and (3,-4) • Find the slope ofthe line on this graph:

  5. Class Exercise: Compute the slope for each pair of points • (0,-3) and (-3,2) • (-2,7) and (3,5) • (0,0) and (60,80) • (4,0) and (7,0)

  6. Class Exercise: • Example 3: Building Stairs p.125

  7. Horizontal Line Equations – 0 Slope

  8. Vertical Line Equations – Undefined Slope

  9. Examples of Vertical Lines Find the slope of 2y = 10

  10. Parallel Lines(Two Lines on the Same Graph with Same Slope)

  11. Slopes of Parallel Linesm1 = m2 One line has a slope of -1/3. A different line passes through the points (-6,2) and (3,-1). Are the lines parallel? Compute the slope of the second line:[2 - -1]/[-6 – 3] = [3]/[-9] = -1/3 (They are Parallel)

  12. Slopes of Perpendicular Linesm1 = -1 / m2

  13. Slopes of Perpendicular Linesm1 = -1 / m2

  14. The Dope on Slope • On a graph, the average rate of change is the ratio of the change in y to the change in x • For straight lines, the slope is the rate of change between any 2 different points • The letter m is used to signify a line’s slopeIf there are two lines, we use m1and m2 • The slope of a line passing through the two points (x1,y1) and (x2,y2) can be computed m=(y2–y1)/(x2–x1) • Horizontal lines (like y=3) have slope 0 • Vertical lines (like x=-5) have an undefined slope • Parallel lines have the same slope m1 = m2 • Perpendicular lines have negative reciprocal slopes m1=-1/m2

  15. What Next? • Present Section 2.4Writing Equations of Lines

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