Question

find a linear function f given f(5) = -1 and f(-5) = -3

Answer 1

linear function means line

they want f(x) = m x + b (that is the equation of a line)
f(5) = -1 means (-1, 5) is a point on the line
f(-5) = -3 tells you a second point on the line

you have two points. Can you find the equation of a line through the two points ?

Answer 2

linear=> f(x)=ax+b
f(5)=a*5+b=-1 -------(1)
f(-5)=a*(-5)+b=-3
-5a+b=-3
b=-3+5a----(2)
putting (2) in (1)
5a-3+5a=-1
10a=2
a=1/5
b=-2

Answer 3

@madams0032