Equation of the Secant Line...1

Find the equation of the secant line given that x = 3 and x = 5?

f(x) = x^2 + 2x

What is a secant line?

 

A secant line, also simply called a secant, is a line passing through two points of a curve.

Find the equation of the secant line given that x = 3 and x = 5?

f(x) = x^2 + 2x

the equation of the secant line: y=mx+b

use x = 3 and x = 5 to find y values of these twq points

f(3) = 3^2 + 2*3=9+6=15.......point (3,15)
f(5) = 5^2 + 2*5=25+10=35.......point (5,35)

y=mx+b ......use point (3,15)

15=m*3+b
15-3m=b..........eq.1

y=mx+b ......use point (5,35)

35=m*5+b
35-5m=b..........eq.2

from eq.1 and eq.2 we have

15-3m=35-5m........solve for m

5m-3m=35-15
2m=20
m=10

so far y=10x+b

use one pint to find b

y=10x+b
15=10*3+b
15-30=b
b=-15

the equation of the secant line:

y=10x-15

 

Not too bad, honestly. Thank you.