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

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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, like y = 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-intercept 3) Use the slope to make a 2 nd point 4) 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

 Two examples  4x + 2y < 4  1) 2) y-intercept: 3) slope: 4) Solid/dotted line: 5) Shade up/shade down: -4x 2y < -4x + 4  2  2  2 y < -2x + 2 2 -2 (down 2, over 1) solid line (solid line underneath <) shade down (<: less than)

 Two examples  - 3 / 2 x – y > 1  1) 2) y-intercept: 3) slope: 4) Solid/dotted line: 5) Shade up/shade down: + 3 / 2 x -y > 3 / 2 x + 1  -1  -1  -1 y < - 3 / 2 x – 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

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