Question

Write a linear function $f$ with $f\left(0\right)=7$ and $f\left(3\right)=1$ .

Answer 1

A linear function will have the form f(x) = mx + b.

f(0)=7 means the point (0,7) is on this line.

f(3)=1 means the point (3,1) is on the line as well.

Using those two points, we can find the slope:

m = (1-7)/(3-0) = -6/3 = -2

Since we were given f(0)=7, we also know the y-intercept.

So our function is f(x) = -2x+7