Question

Let f be a linear function such that f(1)=5 and f(3)=9. Find an equation for f(x)

Answer 1

If f(1)=5 and f(3)=9 we are given two points, so we can use the slope intercept form to find the equation of f(x)

Points:(1,5),(3,9)

Slope intercept form: y2-y1=m(x2-x1)

9-5=m(3-1)
4=m(2)
m=2

f(x)=2x+b Plug in a point and solve for b

5=2(1)+b
3=b

Answer: f(x)=2x+3

Answer 2

`y = 2x + 3`

Explanation:

First, we can find the slope of the line.

`m = (y1-y2)/(x1-x2)\\m=(9-5)/(3-1)\\m = (4)/(2)=2\\`

Using the
`y = mx + b` equation, we can solve for b

`9 = 2(3)+b\\9 = 6 + b\\b = 9-6 = 3`

Let's see if
`y = 2x + 3` works

`2(1) + 3 \\2 + 3 = 5\\\\2(3) + 3\\6 + 3 = 9`

It checks out!