1. Graphing Linear Inequalities
slope & y-intercept
&
x- & y- intercepts
Jeffrey Bivin
Lake Zurich High School
Last Updated: October 11, 2005

2. Graphing Linear Inequalities
Select the desired MENU option below
Slope and y-intercept
x- & y- intercepts
Jeff Bivin -- LZHS

3. Graphing Linear Inequalities
slope and y-intercept
Jeff Bivin -- LZHS

4. y = 2x + 1 y ≤ 2x + 1 1 2 y-intercept b = 1 slope m = 2 Run Rise
Jeff Bivin -- LZHS

5. 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.
Jeff Bivin -- LZHS

6. 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.
Jeff Bivin -- LZHS

7. y = -3x + 2 y ≥ -3x + 2 1 -3 y-intercept b = 2 slope m = -3 Run Rise
Jeff Bivin -- LZHS

8. 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.
Jeff Bivin -- LZHS

9. Run 3
y-intercept
b = -1
Rise 2
slope
Jeff Bivin -- LZHS

10. 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.
Jeff Bivin -- LZHS

11. Graphing Linear Inequalities
x- and y- intercepts
Jeff Bivin -- LZHS

12. 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
Jeff Bivin -- LZHS

13. 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.
Jeff Bivin -- LZHS

14. 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.
Jeff Bivin -- LZHS

15. 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
Jeff Bivin -- LZHS

16. 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.
Jeff Bivin -- LZHS

17. 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
Jeff Bivin -- LZHS

18. 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.
Jeff Bivin -- LZHS

19. 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
Jeff Bivin -- LZHS

20. 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.
Jeff Bivin -- LZHS