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Graphing Linear Inequalities

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The point (1, 1) is NOT a solution to this linear inequality. Substitute 1 for x and 1 for y, and you'll get a statement that is NOT true.
The point (-1, 3) is a solution, since it's in the shaded half-plane. Substitute -1 for x and 3 for y, and you'll get a true statement!
The point (2, 3) is NOT a solution to this inequality. Substitute 2 for x and 3 for y, and you'll get a statement that is NOT true.
The point (-2, 1) is a solution to this inequality since it's in the shaded half-plane. Substitute -2 for x and 1 for y, and you'll get a true statement!
The boundary line is solid because the inequality says "is less than OR EQUAL TO".
The boundary line is dashed because the inequality only says "IS GREATER THAN".
When an inequality is written as y < or y >, the boundary line is dashed. The points on this boundary line are NOT solutions.
When an inequality is written as y ≤ or y ≥, the boundary line is solid. The points on this boundary line ARE solutions.
This shaded half plane represents an inequality that says "y >" since it's shaded ABOVE the boundary line.
This shaded half plane represents an inequality that says "y ≤" since it's shaded BELOW the boundary line.
The slope is 2, and the y-intercept is 1. The line is dashed to indicate an inequality that says "is greater than".
The slope is 1, and the y-intercept is 4. The line is dashed to indicate an inequality that says "is greater than".
The slope is 1, and the y-intercept is -1. The line is solid to indicate an inequality that says "is less than OR EQUAL TO".
The slope is -1, and the y-intercept is 2. The line is solid to indicate an inequality that says "is greater than OR EQUAL TO".
Check out more examples showing what to do when a linear inequality is NOT in slope-intercept form. www.mathsisfun.com
Another lesson on graphing linear inequalities for your viewing pleasure. www.regentsprep.org
Try a quiz! www.regentsprep.org
Graphing linear inequalities on a graphing calculator! mathbits.com
Check out this graph on Desmos.com www.desmos.com
Check out this graph on Desmos.com www.desmos.com
Check out this graph on Desmos.com www.desmos.com
Play with sliders on Desmos.com for y > mx + b www.desmos.com
Play with sliders on Desmos.com for y < mx + b www.desmos.com
Play with sliders on Desmos.com for y ≥ mx + b www.desmos.com
Play with sliders on Desmos.com for y ≤ mx + b www.desmos.com