Graphing Linear inequalities

1. Graphing Linear inequalities • As you probably remember inequalities are regular equations with y and x, but instead of an equal sign they have the inequality sign (> < ≥ ≤ ) • When graphing linear inequalities we will use the same method as we did when graphing things in the form y=mx+b. Meaning: 1st: graph the y intercept (b) 2nd : Find another point by using your slope (m) to count out up or down and over to the right. • However, graphing inequalities have a couple additional steps. 1. The line can be either solid or dotted > and < make dotted lines ≥ and ≤ make solid lines. 2. You have to shade either below or above an inequality line. The way we will find out is to pick a point (x,y) either above or below (not exactly on) and plug in the points to our equation. If the resulting statement is true we shade where the point was (above or below) and if the statement was false we shade away from the point.

2. Example: Graph m= and b=3 Since it is a < symbol we use a dotted line. Now pick any point (x,y) and plug into the equation. I Picked (0,0). and plugged into my equation 0<(0)+3 0<3 Since the statement is true we shade below the line, because our point is below the line.

3. Practice Graphing 1. Y< 2. y ≤ 3x-5 3. 4.

4. Warm-up Graph 1stget y=mx+b: (remember because we divided by a negative 16 we have to flip sign) 2ndgraph B and M. Remember the line is a solid line because of simple. 3rd Shade. Here we shade above the graph (pick a point and plug in)

5. Now lets look at graphing two inequalities on the same graph, and shading to find where they have common solutions. • Example: Graph 1st: Graph the two inequalities 2nd: Shade each inequality (There will be overlap. It helps if you use different colors.) 3rd: The solution is where the 2 shaded areas overlap each other.

6. Writing Inequalities from real life situations: Example: The girls soccer team wants to raise $2000 to buy new goals. They sell sodas for $1 and hotdogs for $1.25. How many of each item do they need to sell to make enough money to buy the goals? A. Write an inequality to represent the situation x= # of sodas sold and y=# of hotdogs sold x($1)+y($1.25) ≥ $2000 (Discuss why this inequality makes sense) B. Graph this inequality Since the inequality is in standard from lets graph it by using x-y intercepts C. Analyze the solution Any coordinates in the shaded area are solutions. The closer the coordinate is to the line to closer the total will be to $2000. The farther above the coordinate is from the line the more the amount will be over $2000. Each line on the graph is 400 units # of hotdogs sold # of sodas sold

7. Homework: Graph the following equations and find where there shaded areas overlap. 1. 2. 3. 4. 5. Mr. Jones would like to spend at most $40 a week on recycling. The trash company he uses charges $1 per pound of plastic and 2$ per pound of paper. a. write an inequality that describes the weekly cost for Mr. Jones to recycle. b. graph the inequality c. what does a point in the shaded area represent? 6. Leah is redecorating her apartment. She can buy paint for $15 a gallon. She can get new linens for $50 each. Leah has $300. a. write an inequality that describes the situation b. graph the inequality c. explain in words what the graph means