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 yintercept? (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