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7.3 Slope-Point Form

7.3 Slope-Point Form. Focus on …. writing the equation of a line from its slope and a point on the line converting equations among the various forms writing the equation of a line from two points on the line solving problems involving equations in slope-point form.

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7.3 Slope-Point Form

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  1. 7.3 Slope-Point Form

  2. Focus on … • writing the equation of a line from its slope and a point on the line • converting equations among the various forms • writing the equation of a line from two points on the line • solving problems involving equations in slope-point form

  3. Investigate Equations in Slope-Point Form 1. Square ABCD in Figure 1 is a composite of four different polygons. The lengths of the sides are shown. What is the area of square ABCD?

  4. What is the new area? P.370-1

  5. Find the slope of each piece

  6. Real problem? • http://www.cut-the-knot.org/Curriculum/Geometry/FibonacciBamboozlement.shtml

  7. It was possible to detect the source of the discrepancy by using the formula for the slope of a line… • The middle pieces do not have the same slope in the second picture… the lines leave a space, creating the difference.

  8. Show how the slope-point form of a linear equation can be developed by using the slope formula,

  9. Example 1 A Line using a Point and the Slope a) Use slope-point form to write an equation of the line through (-2, 5) with slope -3. b) Express the equation in slope-intercept form, y = mx + b.

  10. Solution Substitute -3 for m and the point (-2, 5) for (x1, y1). y - y1 = m(x - x1) y - (5) = -3(x - (-2)) y - 5 = -3(x + 2) The equation in slope-point form is y - 5 = -3(x + 2).

  11. To express the equation in slope-intercept form, isolate y. • y - 5 = -3(x + 2) • y = -3(x + 2) + 5 • y = -3x - 6 + 5 • y = -3x - 1 • In slope-intercept form, the equation is y = -3x - 1.

  12. Your Turn a) Use slope-point form to write an equation of the line through (3, -4) with slope 2. Sketch a graph of the line. b) Express the equation in slope-intercept form, y = mx + b. Sketch a graph of this line. c) Compare your graphs.

  13. Example 2 Determine the Equation of a Line Using Two Points a) Use slope-point form to write an equation of the line through (3, -4) and (5, -1). b) Sketch a graph of the line. c) Rewrite the equation in general form, Ax + By + C = 0.

  14. Assignment • P377 #1 – 7 a,c,e… • #8 – end (even)

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