Question

Explain the steps you take to graph an inequality.

Answer 1

Let's say you had something in the form Ax+By > C

Solving for y would get it into the form y > mx+b only if B is positive.

If B were negative, then the sign would flip and you'd have y < mx+b

For y > mx+b, you shade above the boundary line and y < mx+b has you shade below the boundary line.

The boundary line itself is y = mx+b which goes through two points. Use a solid line if there is an "or equal to" as part of the inequality sign. Otherwise, use a dashed boundary line.

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Examples:

• x+y > 10 solves to y > -x+10. The boundary line is dashed and it goes through (0,10) and (10,0). Shade above the boundary line.
• $4x+2y \le 8$ solves to $y \le -2x+4$. The boundary line y = -2x+4 goes through (0,4) and (2,0). This boundary line is solid. Shade below the boundary line
• x-y > 7 solves to y < x-7. Note the sign flip. The boundary is dashed and it goes through (0,-7) and (7,0). Shade below the boundary line.

An online grapher such as desmos will quickly let you graph any inequality so you can check your work.