graphing inequalities - Solve the following system of inequalities by graphing.

Sangeetha Pulapaka (last edited 4 years ago) (Expert, Educator @Qalaxia)

Step 1:

Write a linear equation for the inequality y < 2 x + 3

The related equation is y = 2 x + 3

Step 2 : Find the x- and the y-intercepts for this equation

For finding x-intercept plug in y = 0 in y = 2 x + 3 to get x = \frac{-3}{2} = 1.5

For finding the y-intercept plug in x = 0 in y = 2 x + 3 to get y = 3

Step 3 : Plot the x- and the y-intercepts on the graph

Plot (-1.5,0) and (0,3) on the graph and join these points to get a straight line

Step 4:

Write a linear equation for the inequality y \leq -4 x + 5

The related equation is y = -4 x + 5

Step 5 : Find the x- and the y-intercepts for this equation

For finding x-intercept plug in y = 0 in y = -4 x + 5 to get x = - 1.25

For finding the y-intercept plug in x = 0 in y = -4 x + 5 to get y = 5

Step 6 : Plot the x- and the y-intercepts on the graph

Plot (-1.25,0) and (0,5) on the graph and join these points to get a straight line

Step 7: Shade the inequalities