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

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

x =

GPT-4o mini · Answer

To find the value of $ x $ for which $ f(x) = g(x) $, we will set the two equations equal to each other. Given: $$ f(x) = -3x + 4 $$ $$ g(x) = 2 $$ We set these equations equal: $$ -3x + 4 = 2 $$ Next, we solve for $ x $: 1. Subtract 4 from both sides: $$ -3x = 2 - 4 $$ $$ -3x = -2 $$ 2. Divide both sides by -3: $$ x = \frac{-2}{-3} = \frac{2}{3} $$ Therefore, the value of $ x $ for which $ f(x) = g(x) $ is: $$ \boxed{\frac{2}{3}} $$