Final answer:
The point of intersection for the functions f(x) = x + 2 and h(x) = 3x - 5 can be found by graphing each equation and identifying where the lines cross, which is at the point (3.5, 5.5).
Step-by-step explanation:
To find the point of intersection using the graphing method for the given functions f(x) = x + 2 and h(x) = 3x - 5, you would plot each function on the same coordinate plane and look for the point where the two lines cross. The equation y = 9 + 3x provided in the references relates to a different problem and does not directly assist us in solving this one.
To graph the two functions, plot the y-intercept and use the slope to determine additional points. For f(x) = x + 2, the y-intercept is 2 (when x = 0), and the slope is 1, indicating a rise of 1 unit up for every 1 unit right. For h(x) = 3x - 5, the y-intercept is -5, and the slope is 3, so for each 1 unit you move to the right, you move 3 units up.
To find the intersection, you can also set the equations equal to each other since at the point of intersection, x and y values will be the same for both equations. This gives us x + 2 = 3x - 5. Solving for x, we subtract x from both sides, getting 2 = 2x - 5, then add 5 to both sides, yielding 7 = 2x. Finally, divide by 2 resulting in x = 3.5. If you plug x = 3.5 into either equation, you'll get the y-coordinate of the intersection, which is y = 3.5 + 2 = 5.5. Therefore, the point of intersection is (3.5, 5.5).