A coordinate plane with 2 lines. The first line is labeled y equals f(x) and passes through (0, 4) and (1, 1) The second line is labeled y - g(x) and is horizontal passing through (negative 2, 2), (0, 2), and (2, 2). The lines intersect at a point that is slightly to the right of (0.5, 2).

Question

If f(x) = −3x + 4 and g(x) = 2, solve for the value of x for which f(x) = g(x) is true.

x = ______________

Answer 1

To solve for the value of x for which f(x) = g(x), we set the two equations equal to each other:

-3x + 4 = 2

Now we can solve for x:

-3x = 2 - 4
-3x = -2
x = -2 / -3
x = 2/3

Therefore, the value of x for which f(x) = g(x) is x = 2/3.