Linear functions
Graphing slope-intercept form worksheets
Graph eight lines in slope-intercept form. Choose graphing alone, graphing with slope and intercept questions, or writing an equation and graph from supplied properties.
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Graphing two-variable inequalities worksheets
Graph eight linear inequalities on coordinate planes. Select any nonempty combination of <, ≤, > and ≥, then draw the boundaries and shade the solution regions with a separate graphical key.
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Draw the boundary line, dashed for a strict comparison and solid when equality is allowed. Test a point off the boundary and shade the matching side.
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A line is the boundary, not the whole answer
Each of the eight prompts describes a set of ordered pairs. The answer key shows a dashed boundary for a strict comparison or a solid boundary when equality is allowed, together with the correct shaded half-plane.
Test a point away from the boundary before choosing the shaded side. The boundary style and the region each carry part of the mathematical meaning.
Learning objective
What this activity builds
Represent all ordered pairs satisfying a linear inequality with a boundary and a half-plane.
Worked example
Graph y ≤ −(1/2)x + 2.
Draw a solid line through (0, 2) and (4, 0), then shade below it.
Equality is included, so the boundary is solid. The test point (0, 0) satisfies 0 ≤ 2, so shade the side containing the origin. The solution contains ordered pairs, not a one-dimensional ray.
Teaching notes
Make the practice count
- Draw the boundary equation before deciding which side to shade.
- Decide line style separately from shading direction.
- Use a test point that is not on the boundary.
- Check one point in each half-plane and one on the boundary.
Make it yours
Customize the practice
Choose your options, update the preview, then download the exact same pages.
Choose one or more comparison signs for eight graphing questions. Every grid uses unit intervals from −5 to 5.
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