Graphing Inequalities Calculator
Enter a linear inequality y (compared to) mx + b to plot the boundary line and shade the solution region.
Graphing a linear inequality means drawing its boundary line y = mx + b and shading the side that satisfies it. Use a dashed line for strict inequalities (< or >) and a solid line for inclusive ones (≤ or ≥). Shade above the line for y > or ≥, and below for y < or ≤.
How to Use This Calculator
Enter the slope and y-intercept of the boundary line, then choose the inequality that relates y to mx + b. The calculator draws the line on a coordinate grid and shades the half-plane of points that satisfy the inequality.
The graph makes the solution set visual: every point in the shaded region is a solution, and the boundary line itself is included only when the inequality is inclusive.
How the Calculation Works
First the boundary line y = mx + b is plotted. It is drawn dashed for a strict inequality (< or >), meaning points on the line are not included, and solid for an inclusive one (≤ or ≥), meaning they are.
Then one side is shaded. For y greater than the line, the region above it is shaded; for y less than the line, the region below. You can confirm the correct side by testing a point such as the origin: if it satisfies the inequality, its side is the one to shade.
draw y = mx + b; dashed if strict; shade above for >/≥, below for </≤
Worked Example
Graph y > x + 2. The boundary is the line y = x + 2, drawn dashed because the inequality is strict. Then shade the region above the line, since y is greater than x + 2.
Test the point (0, 0): is 0 > 0 + 2? No, so the origin is not in the solution — and indeed the origin lies below the line, on the unshaded side, which confirms the shading.
Assumptions and Limitations
- Graphs a single linear inequality in slope-intercept form
- Dashed boundary for strict (< >), solid for inclusive (≤ ≥)
- The grid shows roughly −10 to 10 on each axis
- For systems of inequalities, graph each and overlap the regions
Who Uses a Graphing Inequalities Calculator
Algebra students use this to graph a linear inequality and shade the correct solution region, with a dashed or solid boundary as appropriate. It supports homework and builds intuition for what an inequality looks like on the coordinate plane. Enter the inequality to see it plotted.
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Open calculator →Frequently Asked Questions
When is the boundary line dashed or solid?
Dashed for strict inequalities (< or >), because points on the line are not solutions. Solid for inclusive inequalities (≤ or ≥), because the line itself is part of the solution.
Which side of the line do I shade?
Shade above the line when y is greater than mx + b, and below when y is less. You can check by testing a point like the origin: shade its side if it satisfies the inequality.
How do I graph a linear inequality?
Draw the boundary line y = mx + b (dashed or solid), then shade the half-plane that satisfies the inequality. Every point in the shaded region is a solution.
What does the shaded region mean?
It is the solution set — every point in it makes the inequality true. Points outside it do not, and points on a dashed line are excluded while those on a solid line are included.
How do I graph a system of inequalities?
Graph each inequality on the same axes and shade each region. The solution to the system is where all the shaded regions overlap.
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