Final answer:
To find where the graphs of F(x) = 5x + 1 and G(x) = -2x + 15 intersect, solve for x by setting F(x) equal to G(x) to find x = 2. Then, substituting x back into either equation gives y = 11. Hence, the graphs intersect at (2, 11).
Step-by-step explanation:
The question asks at which point the graphs of the equations F(x) = 5x + 1 and G(x) = -2x + 15 will intersect. To find the intersection point, we set the two equations equal to each other, as the graphs will intersect where their outputs for a particular x-value are the same.
Setting F(x) = G(x) leads to the equation 5x + 1 = -2x + 15. Solving for x, we combine like terms and get 7x = 14, which simplifies to x = 2. Plugging x = 2 back into either of the original equations to solve for y will result in y = 5(2) + 1 = 11. Therefore, the graph of the equations F(x) and G(x) will intersect at the point (2, 11).