Question

Part A: Explain why the x-coordinates of the points where the graphs of the equations y = 4−x and y = 2−x+1 intersect are the solutions of the equation 4−x = 2−x+1. (4 points)
Part B: Make tables to find the solution to 4−x = 2−x+1. Take the integer values of x between −2 and 2. (4 points)

Part C: How can you solve the equation 4−x = 2−x+1 graphically? (2 points)

Answer 1

A: You have 2 equations for y. They will intersect at some point where  "y" is the same for both equations. That is why in equation y=2x+2 you exchange "y" with other equation you got which is y=4x. once you do that you will have

4x=2x+2. 

B: 4x = 2x + 2

   x = -3         -12 = -4   false

   x = -2           -8 = -2   false

   x = -1           -4 = 0    false

   x = 0             0 = 2    false

   x = 1             4 = 4     true

   x = 2             8 = 6     false

   x = 3             12 = 8   false

C. To solve that equation graphically first you draw function y=4x than you draw function y = 2x + 2. After you do that there will be 1 point on graph where functions will intersect. On graph you simply read x value of point where they intersect and that is your solution.