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Secant Lines

Secant Lines. Lesson 1.2.1. Learning Objectives. Given a function and two points, determine the equation, slope, or y-intercept of the secant line. . What is a Secant Line?. Like tangent , the word secant has a meaning in trigonometry, yet has nothing to do with trig in this case.

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Secant Lines

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  1. Secant Lines Lesson 1.2.1

  2. Learning Objectives • Given a function and two points, determine the equation, slope, or y-intercept of the secant line.

  3. What is a Secant Line? • Like tangent, the word secant has a meaning in trigonometry, yet has nothing to do with trig in this case. • Secant line: a line that passes through two points on a function.

  4. Tangent versus Secant • Tangent lines touch (but don’t cross) one point on a function. • Secant lines go through two points on a function.

  5. Finding Slope • To find the slope of a secant line, simply take the two points at which the line crosses, (x1, y1) and (x2, y2), and apply the following formula:

  6. Example 1 A secant line crosses through y = x2 at x = 0 and x = 2. Find its slope.

  7. Now find the equation. • Use point-slope form y – y1 = m(x – x1). • Pick either of your two points for x1 and y1. It does not matter just as long as x1 and y1 match. • Convert into slope intercept form y = mx + b

  8. In the previous example, what was your y-intercept? (Look at your slope-intercept equation. What is b?)

  9. Example 2 • Find the equation of the secant line that passes through f(x) at x = 1 and x = 8

  10. Wrap Up • Know what a secant line is. • Know how to come up with a secant line equation. • Know how to give the slope and y-intercept of a secant line.

  11. Homework • Reteaching

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