Algebra Question

Question

Consider the linear function.

f(x) = -3x+3

The function g(x) has a rate of change of -3 and includes the point (-2,8). What is the difference in the y-intercepts of the two functions, g(0) - f(0), in units?

Answer 1

f(x) = -3x + 3, so the y-intercept is at (0,3)

g(x) has same slope (-3) but goes through (-2,8) and it has a different y-intercept that we need to find.

Substituting: g(x) = mx + b, or 8 = -3(-2) + b

8 = 6 + b, so the y-intercept for g(x) is at (0,2) and g(x) = -3x + 2

The difference in the y-intercepts is -1.

Answer 2

g(x) = -3(x-x₀)+y₀ = -3(x- -2)+8 = -3x-6+8 = -3x+2

g(0)-f(0) = 2-3=-1