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.

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Presentation transcript:

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. Secant line: a line that passes through two points on a function.

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

Finding Slope To find the slope of a secant line, simply take the two points at which the line crosses, (x 1, y 1 ) and (x 2, y 2 ), and apply the following formula:

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

Now find the equation. Use point-slope form y – y 1 = m(x – x 1 ). Pick either of your two points for x 1 and y 1. It does not matter just as long as x 1 and y 1 match. Convert into slope intercept form y = mx + b

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

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

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.

Homework Reteaching