Answer:
f(x) = mx + b
Step-by-step explanation:
f(0) = 5 and f(2) = -3 is a fancy way of writing (0,5) and 2,-3)
Since only 2 points are given, we can form a straight line (i.e., "linear function") of the form f(x) = mx + b, where m is the slope and b is the y-intercept (the value of y when x = 0). I'll use y instead of f(x) for the rest of the problem.
y = mx + b
We can see that one of the points, (0,5) tells us the value of y when x = 0. It is -5, so that is the y intercept.
y = mx - 5
We can calculate the slope from the two points. Slope is "Rise"/"Run", or the change in y for a change in x. The Rise can be calculated:
Going from (0,5) to (2,-3): the Rise is (-3 - (-5)) = -8
The Run is: (2-0) = 2
Rise/Run, or slope, is (-8/2) = -4
y = -4x + 5 is a function that goes through both points.
Or, as the problem fancifully states, f(x) = -4x + 5
