Select the linear function such that it has the indicated function values.

Question

Select the linear function such that it has the indicated function values. ​  ​

Quizplus · Accepted Answer

A linear function has the form f(x) = mx + b, where m is the slope and b is the y-intercept. We are given two function values: f(3) = 10 and f(5) = 14. Using these values, we can set up a system of two equations and solve for m and b:

10 = 3m + b
14 = 5m + b

Subtracting the first equation from the second, we get:

4 = 2m
m = 2

Substituting this value of m into either equation, we get:

10 = 3(2) + b
b = 4

So the linear function is f(x) = 2x + 4. This matches the function values we were given, so the answer is B.

Select the Linear Function Such That It Has the Indicated