Answer:
•Graph linear inequalities in one variable on the coordinate plane.
•Graph linear inequalities in two variables.
•Solve real-world problems using linear inequalities.
Step-by-step explanation:
Yasmeen is selling handmade bracelets for $5 each and necklaces for $7 each. How many of both does she need to sell to make at least $100?
A linear inequality in two variables takes the form
y>mx+b
or
y<mx+b
. Linear inequalities are closely related to graphs of straight lines; recall that a straight line has the equation
y=mx+b
.
When we graph a line in the coordinate plane, we can see that it divides the plane in half:
The solution to a linear inequality includes all the points in one half of the plane. We can tell which half by looking at the inequality sign:
> The solution set is the half plane above the line.
≥
The solution set is the half plane above the line and also all the points on the line.
< The solution set is the half plane below the line.
≤
The solution set is the half plane below the line and also all the points on the line.
For a strict inequality, we draw a dashed line to show that the points in the line are not part of the solution. For an inequality that includes the equals sign, we draw a solid line to show that the points on the line are part of the solution.
Here are some examples of linear inequality graphs. This is a graph of
y≥mx+b
; the solution set is the line and the half plane above the line.
This is a graph of
y<mx+b
; the solution set is the half plane above the line, not including the line itself.
