9.5 Inequalities in Two Variables

Ca 6.0 Sketch the region defined by linear inequalities

Is this ordered pair a solution?

Example 1: Is (5, -3) a solution to 2x – y > 5?

Substitute…

2(5) – (-3) > 5

10 + 3 >5

13 > 5

This is a true statement so, yes, (5, -3) is a solution.

Try this…

1.) Is (2, 1) a solution to x + y < 4?2 + 1 < 4

3 < 4Yes, it is a solution

2.) Is (4,8) a solution to y > 2x + 1?8 > 2(4) + 1

8 > 8 + 18 > 9

No, it is not a solution

Graphing Inequalities in Two Variables

x + y < 41.) Graph the line. (Using

intercepts, two points, or slope intercept form)

Using interceptsX interceptx + 0 < 4x < 4 (4,0)Y intercept0 + y < 4y < 4 (0,4)

x + y < 4

2.) Solid or dashed?

< or > dashed

< or > solid

x + y < 4

3.) Shading?Choose any point on the

coordinate plane. If it is a solution to the inequality you shade the region where that point is, if not, then shade the opposite region.

I choose (0, 0)0 + 0 < 40 < 4,true, so I will shade

below the line

Graph y – 2x > 0

Using slope intercept.

y – 2x > 0

+ 2x + 2x

y > 2x

y intercept is (0, 0)

Slope is 2

y > 2x

2.) Solid line because of the >

3.) I am going to try the point (2,0)

0 > 2(2)

0 > 4

No, so shade above the line

Try this…

Graph y > x – 1