Question

How can you solve the equation 4−x = 2x + 3 graphically?

Answer 1

Explanation:

Graph the two lines separately but on the same graph paper, and then from the completed graph read off the coordinates of the point of intersection.

y = 4 - x has a y-intercept of 4 and a slope of -1. Plot the point (0, 4) and then draw a line with slope -1 through it.

y = 2x + 3 has a y-intercept of 3 and a slope of 2. Plot (0, 3) and then draw a line with slope +2 through it.

As a check, solve for x and y algebraically:

4 - x = 2x + 3 becomes 1 - x = 2x, or 3x = 1. Then x = 1/3.

Use y = 4 - x to find the y value when x = 1/3:

y = 4 - 1/3 = 11/3

Thus, the solution is (1/3, 11/3)

Answer 2

x = 1/3

Explanation:

Hello,

we can draw the two lines defined by

y = 4 - x

y = 2x + 3

And search for the intersection point as below

This is the point A (1/3, 11/3)

Do not hesitate if you have any question

Thanks