whats the answer to this linear function f(4)=9 and f(-4)=-7

Question

i need help with this question for my homework assignment

Answer 1

The values inside the parentheses are our inputs, and the values outside are our output. That means if 4 is our x, 9 is our y:

(4, 9), and similarly (-4, -7)

From here, we use the slope formula:

^{y2 - y1} / _{x2 - x1}:

^{(-7 - 9)} / _{(-4 - 4)}

m = -16 / -8

m = 2

 

So that means so far we have f(x) = 2x + b. Now we can use an ordered pair to find b:

f(4) = 2 * 4 + b

f(4) = 9:

9 = 2* 4 + b

9 = 8 + b

1 = b

 

Check:

-7 = 2 * -4 + 1

-7 = -8 + 1

-7 = -7