Just as a picture is worth a thousand words, a graph is sometimes better than an equation.
Jenn, Founder Calcworkshop®, 15+ Years Experience (Licensed & Certified Teacher)
Such is the case with linear inequalities.
When graphing inequalities in two variables it is important to note that the coordinate plane is divided into three sets of points…
… the points on the line
… the points above the line
… the points below the line.
These two regions (above or below the line) are called half-planes whereas the line itself is referred to as the boundary.
Why does this matter?
Because the solution to an inequality includes more than just the line or boundary, but all the points either above or below the line that makes the inequality statement true.
Together we will look at the three simple steps for how to graph linear inequalities.
Graph of Two Linear Inequalities
First, we need to solve the inequality for slope-intercept form.
Or more simply, get y on the left and everything else on the right, as Math is Fun deftly states.
Next, we sketch the line using a dotted line for less than or greater than, and a solid line for less than or equal to or greater than or equal to.
And finally, we shade the appropriate region by choosing a test point, not on the boundary, that satisfies the inequality.
All this means is that we will pick a point, not on the line, and plug it into the inequality. If the statement is true, then we shade the region containing this point. If the statement is false, then we shade the region on the other side of the line.
Graphing Linear Inequalities – Video
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