Questions: Solve the following equation using a graphical method. 5(x-8)=7(x-4)+4 Graph the left side of the equation as y1 and the right side as y2 on the same viewing window. Choose the correct graph below. All graphs have viewing window [-15,15] by [-100,100] with Xscl=1 and Yscl=10. A. B. C. D.

Solution Steps

First, simplify the given equation:

5(x - 8) = 7(x - 4) + 4 5x - 40 = 7x - 28 + 4 5x - 40 = 7x - 24 -16 = 2x x = -8

Define y1 and y2 as follows: y1 = 5(x - 8) = 5x - 40 y2 = 7(x - 4) + 4 = 7x - 24

Graphically, the solution to the equation is the x-coordinate of the intersection point of the lines y1 and y2. Since we already solved for x algebraically (x = -8), we look for the graph where the two lines intersect when x = -8. We can find the corresponding y-values:

y1 = 5(-8) - 40 = -80 y2 = 7(-8) - 24 = -80

So, the intersection point is (-8, -80).

Given the viewing window [-15, 15] by [-100, 100], we should see an intersection point at (-8,-80). Graph C correctly displays the lines intersecting at the correct point.

Final Answer: The correct graph is C.