Graphing Inequalities in Two Variables ALGEBRA 1 UNIT 6: INEQUALITIES.

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Presentation transcript:

Graphing Inequalities in Two Variables ALGEBRA 1 UNIT 6: INEQUALITIES

Graphing Equations

 Graph the equation:  Y = 4x + 3

Graphing Equations  Graph the equation:  Y = 4x + 3  Step 1: Create an x/y chart  Step 2: Pick two points for x  Step 3: Determine the value of y given x  Step 4: Graph the two points and draw the line.

Graphing Equations Practice  Graph the equation:  Y = -5x – 2

Graphing Equations Practice  Graph the equation:  Y = -5x – 2  Step 1: Create an x/y chart  Step 2: Pick two points for x  Step 3: Determine the value of y given x  Step 4: Graph the two points and draw the line.

ASSIGNMENT  With the two sticky- notes you have, there are 6 equations you will graph on the given graph paper. I need these turned in tomorrow!

Graphing Inequalities

Graphing Inequalities Basic Steps  Step 1: Create an x/y chart  Step 2: Pick two points for x.  Step 3: Determine the value of y, given x.  Step 4: Graph the two points and draw the line:  ******* IF >,< then it is a DOTTED LINE!!  ******* IF ≥, ≤ then it is a SOLID LINE!!  Step 5: Determine which side to shade (shading test explained later).

Shading  Determining what side to shade:  Step 1: Pick a point not on the line. (0,0) is usually the easiest.  Step 2: Plug those coordinates into the equation.  Step 3: Determine if the statement is a true or false statement.  Step 4: Shade the same side of the line as the point if a TRUE Statement. Shade the opposite side of the line as the point if a FALSE statement.

Graphing Inequalities  Y < 2x + 1

Graphing Inequalities  Y < 2x + 1  Step 1: Create an x/y chart  Step 2: Pick two points for x  Step 3: Determine the value of y given x  Step 4: Graph the two points and draw the line.  Step 5: Shade (detailed on next slide)

Shading  Determining what side to shade:  Step 1: Pick a point not on the line. (0,0) is usually the easiest.  Step 2: Plug those coordinates into the equation.  Step 3: Determine if the statement is a true or false statement.  Step 4: Shade the same side of the line as the point if a TRUE Statement. Shade the opposite side of the line as the point if a FALSE statement.

Graphing Inequalities  Y < 2x + 1  Step 1: Pick (0,0)  Step 2: 0 < 2(0) + 1  Step 3: 0 < 1 TRUE statement  Step 4: Shade the same side as the point.

Graphing Inequalities Practice  Graph:  Y ≥ -3x - 2

Graphing Inequalities Practice  Graph:  Y ≤ ¼ x + ½