1. Graphing a Linear Inequality
Graphing a linear inequality is very similar to graphing
a linear equation.

2. Graphing Linear Inequalities
slope & y-intercept
&
x- & y- intercepts

3. Graphing Linear Inequalities
Select the desired MENU option below
Slope and y-intercept
x- & y- intercepts

4. Graphing Linear Inequalities
slope and y-intercept

5. y = 2x + 1
y ≤ 2x + 1
Run 1
y-intercept
Rise
b = 1 2
slope
m = 2

6. y = 2x + 1 y ≤ 2x + 1 Shade TRUE 1 ≤ 2(2) + 1 1 ≤ 4 + 1 1 ≤ 5
Now for the shading
Pick a point on either side of the graph
Let’s try (2, 1)
Does the point satisfy the inequality?
Shade
1 ≤ 2(2) + 1
1 ≤ 4 + 1
TRUE
1 ≤ 5
Therefore, shade the half-plane with the point.

7. y = 2x + 1 y ≤ 2x + 1 Don't Shade Shade FALSE 3 ≤ 2(-2) + 1 3 ≤ -4 + 1
What if we picked a point on the other side of the line?
Don't Shade
Let’s try (-2, 3)
Does the point satisfy the inequality?
Shade
3 ≤ 2(-2) + 1
3 ≤
3 ≤ -3
FALSE
Therefore, shade the other half-plane opposite the point.

8. y = -3x + 2
y ≥ -3x + 2
Run 1
y-intercept
Rise
b = 2 -3
slope
m = -3

9. y = -3x + 2 y ≥ -3x + 2 Shade Don't Shade FALSE 0 ≥ -3(0) + 2
Now for the shading
Pick a point on either side of the graph
Let’s try (0, 0)
Shade
Does the point satisfy the inequality?
Don't Shade
0 ≥ -3(0) + 2
0 ≥ 0 + 2
FALSE
0 ≥ 2
Therefore, shade the other half-plane opposite the point.

10. Run 3
y-intercept
b = -1
Rise 2
slope

11. Shade TRUE Now for the shading Let’s try (0, 0)
Pick a point on either side of the graph
Let’s try (0, 0)
Shade
Does the point satisfy the inequality?
TRUE
Therefore, shade the half-plane with the point.

12. Graphing Linear Inequalities
x- and y- intercepts

13. 2x + 3y ≥ 5 find the x value when y = 0 find the y value when x = 0
x-intercept
2x + 3(0) = 5
2x + 0 = 5
2x = 5
find the y value
when x = 0
y-intercept
2(0) + 3y = 5
0 + 3y = 5
3y = 5

14. 2x + 3y ≥ 5 Shade TRUE Now for the shading Let’s try (4, 2)
Pick a point on either side of the graph
Let’s try (4, 2)
Shade
Does the point satisfy the inequality?
TRUE
Therefore, shade the half-plane with the point.

15. 2x + 3y ≥ 5 Shade Don't Shade FALSE
What if we picked a point on the other side of the line?
Let’s try (-3, -4)
Shade
Does the point satisfy the inequality?
Don't Shade
FALSE
Therefore, shade the other half-plane opposite the point.

16. 4x - y > 6 find the x value when y = 0 find the y value when x = 0
x-intercept
4x - (0) = 6
4x - 0 = 5
4x = 6
find the y value
when x = 0
y-intercept
4(0) - y = 6
0 - y = 6
-y = 6

17. 4x - y > 6 Don't Shade Shade FALSE Now for the shading
Pick a point on either side of the graph
Let’s try (0, 0)
Does the point satisfy the inequality?
Don't Shade
Shade
FALSE
Therefore, shade the other half-plane opposite the point.

18. 4x + 2y < 3 find the x value when y = 0 find the y value when x = 0
x-intercept
4x + 2(0) = 3
4x + 0 = 3
4x = 3
find the y value
when x = 0
y-intercept
4(0) + 2y = 3
0 + 2y = 3
2y = 3

19. 4x + 2y < 3 Shade TRUE Now for the shading Let’s try (0, 0)
Pick a point on either side of the graph
Let’s try (0, 0)
Does the point satisfy the inequality?
Shade
TRUE
Therefore, shade the half-plane with the point.

20. 3x - 2y < 7 find the x value when y = 0 find the y value when x = 0
x-intercept
3x - 2(0) = 7
3x - 0 = 7
3x = 7
find the y value
when x = 0
y-intercept
3(0) - 2y = 7
0 - 2y = 7
-2y = 7

21. 3x - 2y < 7 Shade TRUE Now for the shading Let’s try (0, 0)
Pick a point on either side of the graph
Let’s try (0, 0)
Does the point satisfy the inequality?
Shade
TRUE
Therefore, shade the half-plane with the point.