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