# How do you find the equation of the secant line of #f(x)=x^2-5x# through the points [1,8]?

##### 2 Answers

The line will pass through the points

The line will pass through the points

The slope is

The point-slope form of the equation of a line is:

Substitute

#### Explanation:

We have

When

#x=1 => f(x) = 1-5 = -4#

When#x=8 => f(x) = 64-40 = 24#

So the required secant line passes through the points

We can calculate the slope of the secant line using

#m=(Delta y)/(Delta x) = (24-(-4)) / (8-1) = 28/7 = 4#

So using the factthat the line passes through

# y - (-4)=4(x-1) #

# :. y +4 = 4x-4 #

# :. y = 4x-8 #

NB: We could have equally used the other coordinate

Which we can confirm graphically: