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, (x1, y1) and (x2, y2), and apply the following formula:

Example 1

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

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

• 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