Question

2x + y ≤ 2

a. change the inequality into slope-intercept form, and then change it into an equation.

b. create a table. Use the x-values indicated

c. Graph the points and draw a line.

d. Shade the solution area.

e. Check your solution. Use (0,0) as your test point and see if it satisfies the conditions of the original inequality.

Answer 1

a. To change the inequality into slope-intercept form, we need to solve for y:

2x + y ≤ 2

y ≤ -2x + 2

To change it into an equation, we remove the inequality symbol and obtain:

y = -2x + 2

b. Using the x-values indicated, we can create a table of corresponding y-values:

|x | y |
|---|---|
|0 | 2 |
|1 | 0 |
|2 |-2 |

c. To graph the points and draw a line, we plot the points (0, 2), (1, 0), and (2, -2) on the coordinate plane and connect them with a straight line.

d. To shade the solution area, we need to determine which side of the line satisfies the inequality. Since the inequality is less than or equal to, we shade the area below the line.

e. To check the solution, we plug in the test point (0, 0) into the original inequality:

2x + y ≤ 2

2(0) + 0 ≤ 2

0 ≤ 2

The inequality holds, so the point (0, 0) is in the shaded area and satisfies the conditions of the original inequality. Therefore, the solution is valid.