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Rates of Change (Slope)

Rates of Change (Slope). Section P.2. After this lesson, you should be able to:. find the slope of a line passing through two points write the equation of a line given the point and the slope sketch the graph of a linear equation in slope-intercept form

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Rates of Change (Slope)

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  1. Rates of Change (Slope) Section P.2

  2. After this lesson, you should be able to: • find the slope of a line passing through two points • write the equation of a line given the point and the slope • sketch the graph of a linear equation in slope-intercept form • write equations of lines that are parallel or perpendicular to a given line

  3. rise change in y = = run change in x m = where Slope of a Line Slope: Also, A line has the same slope everywhere.

  4. Equations of Lines To write the equation of a line, you need: • one point • the slope Remember: Equations of lines are first degree equations.

  5. Point-Slope Equation of a Line Given the slopem passing through the point , an equation of the line can be written in the form

  6. Example Example: Find an equation of a line that has a slope of 4 and passes through the point (-2, 3).

  7. Examples of Horizontal and Vertical Lines Example: Find an equation of a vertical line that passes through the point (-2, 6). Example: Find an equation of a horizontal line that passes through the point (-2, 6).

  8. In this case, m = 2 b = 1 y to the right 1 up 2 x Graphing Lines Using Slope-Intercept Method Example: Sketch the graph of using the slope-intercept method. m = slope b = y-intercept

  9. y y x x More Examples of Lines Ex: Sketch the graph of Ex: Sketch the graph of This will be a _______________ line with a __-intercept of 3. This will be a ____________ line with an ____-intercept of -2. Note: This is not a function What is the slope of the line? What is the slope of the line?

  10. Summary of Lines • General form: Ax + By + C = 0 • Vertical line: x = a • Horizontal line: y = b • Point-slope form: y – y1 = m(x –x1) • Slope-intercept form: y = mx + b

  11. Parallel and Perpendicular Lines Two distinct nonvertical lines are parallel iff their slopes are____________________. Two distinct nonvertical lines are perpendicular iff their slopes are _______________ _________________ of each other.

  12. Example-Parallel Line Example: Write an equation of the line that is parallel to the line x +y = 7and passes through the point (-3, 2).

  13. Example-Perpendicular Line Example: Write an equation of the line that is perpendicular to the line x +y = 7and passes through the point (-3, 2).

  14. Another Example— Parallel and Perpendicular Lines Find the general form equation of the line that passes through and is a) parallel to b) perpendicular to

  15. Homework Section P.2: pages 16- 17#1-5 odd, 15-19 odd, 23-29 odd, 35, 37, 39, 43, 57-61 odd, 69, 71

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