Graphing Inequalities Math Example 2

Follow the full solution, then compare it with the other examples linked below.

Example 2

medium
Graph the solution of y≤2x+1y \leq 2x + 1 on the coordinate plane.

Solution

  1. 1
    Graph the boundary line y=2x+1y = 2x + 1 as a solid line (≤\leq includes the boundary).
  2. 2
    Test the point (0,0)(0, 0): 0≤2(0)+1=10 \leq 2(0) + 1 = 1. True ✓
  3. 3
    Shade the region containing (0,0)(0, 0)—below the line.

Answer

Solid line y=2x+1y = 2x + 1, shade below.
To graph a linear inequality: (1) draw the boundary line (solid for ≤/≥\leq/\geq, dashed for </></>), (2) test a point not on the line, (3) shade the side that satisfies the inequality.

About Graphing Inequalities

The process of representing the solution set of an inequality on a coordinate plane by drawing the boundary line (solid for ≤\leq/≥\geq, dashed for <</>>) and shading the half-plane that contains all points satisfying the inequality.

Learn more about Graphing Inequalities →

More Graphing Inequalities Examples

Example 1 easy

Graph [formula] on a number line.

Example 3 easy

Graph [formula] on a number line.

Example 4 medium

Is the point [formula] in the solution region of [formula]?

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