Show the region represented by 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.
Rewrite the equation in the form y = mx + c.
From the equation m will be the gradient and c 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.
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.
Show the region represented by the inequality x + y < 1
Rewrite the equation x + y = 1in the form y = mx + c.
x + y =1 ⇒ 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.
Graphing Linear Inequalities Lesson
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