Given f(x) is a linear equation, with f(−3)=12, and slope m =−2, what is the equation for the line in standard form?

Answer 1

A linear equation fits the form of y = mx + b, or using function notation, f(x) = mx + b

If f(-3) = 12 then when x = -3, f(x) = 12 or y = 12 so the point on the line is (-3, 12).

For m = -2, then f(x) = -2x + b and using the point (-3, 12) we can say:

12 = -2(-3) + b

12 = 6 + b

b = 6

So f(x) = -2x + 6