f (0) = -7, f (7) = 1

Question

write a linear function with the given values. I need help! We do not understand this level of math!

Answer 1

have (are given) two pairs of (x,f(x)), where y(x) is the same as f(x)

pair#1, (0,-7) which is a point on the xy plane

pair#2, (7,1) also a point on xy plane

the slope of the line connecting point 1 with point 2 is

m=(1-(-7))/(7-0)=(y₂-y₁)/(x₂-x₁)=(8/7)

abstractly, any x, y(x) pair on line will have

m=(y-y₁)/(x-x₁)

here

8/7=(y-(-7))/(x-0)

or

y=(8/7)x-7 is the line going through both points

check,,,,x=7, y=1

Answer 2