A linear equation is graphed as a line whereas a linear inequality is graphed as a line and a shaded region.
In the following diagram,
We can graph linear inequalities in the following way:
Step 1: Rewrite the inequality as an equation. Draw the line that represents the equation. (Review Graphing Linear Equations if necessary.) Draw a solid line if the inequality is ≤ or ≥. Draw a dashed line if the inequality is < or >.
Step 2: Pick a point NOT on the line and substitute in the x and y values of the point into the inequality. If the point makes the inequality true, shade that side of the line. If the point makes the inequality false, shade the opposite side of the line.
Graph the inequality 2x – 3y ≥ 6
First, we need to draw the line 2x – 3y = 6.
We will revise the method for drawing a straight line using slope-intercept form.
Rewrite the equation in the form y = mx + b. From the equation m will be the gradient and b will be the y-intercept.
2x – 3y = 6
y = x – 2
The gradient is then and the y-intercept is – 2.
If the inequality is ≤ or ≥ then we draw a solid line. If the inequality is < or > then we draw a dotted line. Since the given inequality is ≥, we draw a solid line.
After drawing the line, we need to shade the region.
We pick a point not on the line, for example (0, 0). We substitute (0, 0) into the inequality 2x – 3y ≥ 6 and finds that it is false. So, we shade the opposite side of the line.The following diagram shows how to graph the linear inequality 2x - 3y ≥ 6. Scroll down the page for more examples of graphing linear inequalities.
Graph the inequality x + y > 1
Rewrite the equation, x + y = 1, in the form y = mx + b.
x + y = 1 can be written as y = –x + 1
The gradient is then –1 and the y-intercept is 1.
We need to draw a dotted line because the inequality is >.
After drawing the dotted line, we need to shade the region.
We pick a point not on the line, for example (0, 0). We substitute (0, 0) into the inequality x + y > 1 and finds that it is false. So, we shade the opposite side of the line.
The following videos shows how to graph linear inequalities.How to Graph Linear Inequalities?
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