Essential Question: When graphing an inequality, how do you determine whether to include the boundary in the graph and which region to shade?

A linear equation contains two variables, likey = ½ x – 1

A linear inequality looks the same, except the equal sign is replaced with an inequality:

< < > or >Linear inequalities can ONLY be

solved by graphing

To graph a linear inequality:1) Solve for y (get y by itself)▪ Make sure y is on the left

2) Plot the y-intercept3) Use the slope to make a 2nd point4) Draw the line▪ > or <: dotted line▪ > or <: solid line (solid line underneath = use

solid line)

5) Shade your solution area▪ > or >: shade above your line▪ < or <: shade below your line

1 2 3 4 5–1–2–3–4–5 x

1

2

3

4

5

–1

–2

–3

–4

–5

y Two examples 4x + 2y < 4

1) 2)y-intercept: 3)slope: 4)Solid/dotted line:5)Shade up/shade down:

-4x -4x

2y < -4x + 42 2 2y < -2x + 2

2-2 (down 2, over 1)

solid line (solid line underneath <)shade down (<: less than)

1 2 3 4 5–1–2–3–4–5 x

1

2

3

4

5

–1

–2

–3

–4

–5

y Two examples -3/2 x – y > 1

1) 2)y-intercept: 3)slope: 4)Solid/dotted line:5)Shade up/shade down:

+3/2x +3/2x

-y > 3/2x + 1-1 -1 -1y < -3/2x – 1

-1-3/2 (down 3, over 2)

dotted line (no line underneath <)shade down (<: less than)

Divide by a negative?Flip the inequality

Assignment Page 102 Problems 1 – 9 & 23 – 24, all