1. Linear Inequalities

2. When you replace the equals sign in a linear equation by one of the inequality symbols, you now have a linear inequality.
Examples: 1 2
y >
x + 1
2x – 3y < 12

3. Any ordered pair of numbers that satisfies the inequality is a solution of the inequality.
Just like an inequality in one variable, linear inequalities can have infinitely many solutions.

4. y < x + 1
Run 1
y-intercept
Rise 1
b = 1
slope
m = 1

5. y < x + 1 y = 2x + 1 Shade TRUE 0 < 0 + 1 0 < 1
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?
0 < 0 + 1
TRUE
Therefore, shade the half-plane with that point.
0 < 1

6. y < x + 1 y = 2x + 1 Don't Shade Shade FALSE 2 < - 3 + 1
What if we picked a point on the other side of the line?
Now try (-3, 2):
Does the point satisfy the inequality?
Shade
2 <
2 < - 2
FALSE
Therefore, shade the half-plane opposite that point.

7. 4x - 3y > 12 find the x value when y = 0 find the y value
x-intercept
4x - 3(0) = 12
4x - 0 = 12
4x = 12
x = 3
find the y value
when x = 0
y-intercept
4(0) - 3y = 12
0 - 3y = 12
-3y = 12
y = -4

8. 4x - 3y > 12 Don't Shade Shade FALSE 4(0) - 3(0) > 12
Now for the shading . . .
Pick a point on either side of the graph.
Don't Shade
Let’s try (0, 0):
Does the point satisfy the inequality?
Shade
FALSE
4(0) - 3(0) > 12
0 - 0 > 12
Therefore, shade the other half-plane opposite the point.
0 > 12