Warm Up Graph each inequality. 1. x > –5 2. y ≤ 0 3. Write –6x + 2y = –4 in slope-intercept form, and graph. y = 3x – 2

Graphing Linear Inequalities in Two Variables

Solution or No Solution? That is the question!

Graphing by Using Slope and y-intercept Graph the line given the slope and y-intercept. y intercept = 4 Step 1 The y-intercept is 4, so the line contains (0, 4). Plot (0, 4). Step 3 Draw the line through the two points. Run = 5 Rise = –2 Step 2 Slope = Count 2 units down and 5 units right from (0, 4) and plot another point. y

Graphing Linear Inequalities Four simple things to remember! 1.A dotted line is like an open circle ( ) 2.A solid line is like a closed circle ( ) 3.“Greater than” is above ground 4.“Less than” is below ground Okay then, here we go…

A linear inequality in x and y is an inequality that can be written as follows. ax + by < c ax + by ≤ c ax + by > c ax + by ≥ c The graph of a linear inequality in two variables is the graph of the solutions of the inequality. A line divides the coordinate plane into two half- planes. The solution of a linear inequality in two variables is a half-plane.

Graphing a Linear Inequality 1.Graph the corresponding equation (in slope- intercept form). Use a dashed line for inequalities with > or < to show that the points on the line are NOT solutions. Use a solid line for inequalities with ≥ and ≤ to show that the points on the line ARE solutions.

2.The line you drew separates the coordinate plane into two half-planes. Test a point in one of the half-planes to find whether it is a solution of the inequality. 3.If the test point IS a solution, shade the half- plane it is in. If not, shade the other half- plane. (Hint: If it is > or ≥, you will shade above the line. If it is < or ≤ you will shade below the line)

Sketch the graph of the Inequality 3x – y > 5 First solve for y -y > -3x + 5 y < 3x – 5 Graph the equation like y = 3x – 5 except use a dotted line for the graph. Substitute (0,0) in the equation. 0< 3(0) – 5 0 < -5 False “Shade” the half-plane that does not include (0, 0)

Sketch the graph of the Inequality -x + y ≤ 3

Sketch the graph of the Inequality 9x – 3y < 18

Sketch the graph of the Inequality y – 5x ≥ 0

Warm up