Algebra 1 Practice - Graph a Linear Inequality on a Coordinate Plane (Example 5)
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1. Write the Inequality in Standard Form
Ensure the inequality is in the form where you have one side of the inequality compared to the other side. For example:
𝑦
≥
2
𝑥
+
3
y≥2x+3
2. Graph the Corresponding Linear Equation
Rewrite the Inequality as an Equation:
Convert the inequality into an equation by replacing the inequality symbol with an equal sign:
𝑦
=
2
𝑥
+
3
y=2x+3
Plot the Line:
Find and plot the y-intercept (where the line crosses the y-axis).
Use the slope to determine another point on the line. For instance, if the slope is 2, it means that for every 1 unit you move to the right, you move 2 units up.
Draw the line through the points you plotted. The line can be solid or dashed.
Solid Line: If the inequality includes "is greater than or equal to" or "is less than or equal to," use a solid line to indicate that points on the line are included in the solution.
Dashed Line: If the inequality includes "is greater than" or "is less than," use a dashed line to indicate that points on the line are not included in the solution.
3. Determine the Shading Region
Choose a Test Point:
Pick a point not on the line, such as the origin (0, 0), to test which side of the line satisfies the inequality. Substitute this point into the original inequality.
Shade the Appropriate Region:
If the point satisfies the inequality, shade the region that includes this point.
If the point does not satisfy the inequality, shade the opposite side of the line.
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Nick Perich
Norristown Area High School
Norristown Area School District
Norristown, Pa
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