Question

Part A: Explain why the x-coordinates of the points where the graphs of the equations y = 4−x and y = 2x + 3 intersect are the solutions of the equation 4−x = 2x + 3. (4 points) Part B: Make tables to find the solution to 4−x = 2x + 3. Take the integer values of x between −3 and 3. (4 points) Part C: How can you solve the equation 4−x = 2x + 3 graphically? (2 points)

Answer 1

Try this explanation:

A: The property of intersection point is: on the graphs it belongs to the first line and to the second line, in another word, it belongs to the both lines. 'To the both lines; means, for the both equations, this value of 'x' converts the left side and the right side to the same value (one value 'x' ⇒ one value on the left part and the same value on the right part of the equation 4-x=2x+3).

B: see the attachment, based on 4 steps.

C: see the attached graph. The intersection point is marked with green colour.