Find a liner equation f(x) with slope 5 such that f(3)=12

Using f(x) the formula would be f(x) = 5x + b. The standard form of the slope intercept formula is

y = mx + b. The slope is represented by m, which equal 5. Since you know that f(3) = 12, the only unknown is b. So you simply plug in the known information and solve.

y = mx + b

12 = 5(3) + b

12 = 15 + b

Subtract 15 from both sides.

b = -3

Prove the formula.

12 = 5(3) - 3

12 = 15 - 3

12 = 12