Question

Write an equation for a linear function f that has the given values: f(-3) = 2 and f(1) = 0

Answer 1

A linear function can be written in this form: 

y - y2 = m(x - x2) 


f(-3) = 2 
f(-3) is saying that some function had the number -3 put in for the value of x. The output was a value of 2. Which is our y. So we have a coordinate point of: 
(-3, 2) 

Same thing with f(1) = 0 

(1,0) 

Now we need to find the slope, m. 

(2 - 0) / (-3 - 1) = 2 / -4 = -1/2 

So an equation for the linear function f is this: 
y - 2 = -1/2(x + 3) 

(Note that the -3 we subbed in has become a positive 3 because the equation called for a negative. And two negatives become a positive)