Graph inequalities in two variablesWrite from a graph
Name: Date:
Write the inequality each graph shows. A dashed line is not included.
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Write the inequality from a graph worksheets
Reading a graph backward asks for everything graphing did, in the opposite order. These free printable worksheets show a shaded region and ask for the inequality that made it, with an answer sheet.
If they get stuck
Write the inequality from a graph
The answer key prints on a separate page.
What's on this sheet
The line comes first. Read where it crosses the y-axis and how steeply it climbs, and write its equation as if the sign were an equals sign. Then decide the sign in two steps. A dashed line means no bar and a solid line means a bar, and that settles half of it.
Why this sheet works
A test point settles the direction. If (0, 0) is in the shading, the finished inequality has to be true there. So try the sign and see: with the line y = 2x − 1, the point (0, 0) gives 0 ≥ −1, which is true, so ≥ is right if the shading covers it. If (0, 0) is outside the shading, the inequality has to come out false there instead.
How this one works
Write the inequality this graph shows.
y = −2x + 2
y < −2x + 2
- Read the line. It crosses the y-axis at 2 and its slope is −2, so its equation is y = −2x + 2.
- The line is dashed, so the sign has no bar. (0, 0) is in the shading, so it has to make the inequality true, and 0 < 2 is true. That picks the direction: y < −2x + 2.