3 5 graphing linear inequalities in two variables

3.5 Graphing Linear Inequalities in Two Variables

What is a Linear Inequality?•An inequality containing x and y whose boundary is a straight line.

Checking Solutions•Solutions of linear inequalities are ordered pairs (x, y) that make the inequality true. •To check if a point is a solution:▫Plug it in for x and y▫Simplify▫Does it make a true statement?

Example•Is (-1, 9) a solution of 2x + y < -3 ?

Example•Is (2, -2) a solution of x – 3y ≥ 8 ?

Example•Is (-3, 4) a solution of y > -1 ?

Example•Is (0, 0) a solution of y > x ?

You Try!•Is (-4, -1) a solution of 5x – 2y ≤ -1?

Graphs of Linear Inequalities•Linear inequalities, like linear equations, cannot be “solved” to get a number answer.•Instead, we use a graph to show all solutions!•Graphs will contain a “boundary line” and a shaded “half plane.”

Dashed or Solid•A dashed line means points on the line are not solutions.▫Use for < and >.

•A solid line means points on the line are solutions.▫Use for ≤ and ≥.

Where to Shade?•The shaded area shows all possible points that make the inequality true.•Test a point.▫We usually use (0,0).▫If it is on the line, choose a different point.

•If it is a solution, shade that side.•If it is not a solution, shade the other side.

Graphing Simple Linear Inequalities•Linear inequalities with only one variable have horizontal or vertical boundary lines.•x: vertical (up and down)•y: horizontal (side to side)

Example:•Graph y ≤ 2.

Example:•Graph x > 1.

Example:•Graph y ≥ -5.

You Try!Graph y > -1 Graph 3.5 > x

Slope-Intercept Form•Remember: y = mx + b•m = slope ▫rise over run!•(0, b) = y-intercept

Example•Graph y ≤ 3x – 1

Example•Graph y > ½ x + 3

Example•Graph y ≥ - x – 2

You Try!•Graph y < x + 2

Standard Form•Remember: ax + by = c•Two choices:▫Solve for y. Rewrite as y = mx + b.

- or -▫Find intercepts: (0, y) and (x, 0)

Graphing Practice/Review•Graph 3x + 2y = -6 both ways.

Example•Graph –x + 2y > 2

Example•Graph 3x – 2y < 6

Example•Graph 3x – 2y ≥ 0

You Try!•Graph –x + 4y > – 2