Graphs and Functions

Question

Given g(x)=x^2-9x, find the equation of the secant line passing through (-3, g(-3)) and (5, g(5)). Write your answer in the form y=mx+b.

Answer 1

x^2 -9x = g(x)

g(-3) =9+27 = 36

(-3, g(-3)) = (-3,36)

g(5) = 25-45 = -20

(5,g(5)) = (5,-20)

line through the two points has slope ="rise over run" = change in y over change in x = (36+20)/(-3-5) = -56/8 =-7

the line's equation is

y+20 = -7(x-5) in point slope form

or use the other point

y-36 = -7(x+3)

or

y = -7x+35-20

y =-7x+15 in slope intercept form ***

that's the "y=mx + b" form,

that you want, where m=-7= the slope

and b = 15 = the y intercept

or

7x+y = 15 in standard form

it may help to plot the 2 points and connect them with a straight line