Practice Graphing Linear Inequalities

Front

What is a linear inequality?

Back

A linear inequality is a mathematical statement that relates a linear expression to a value using inequality symbols (>, <, ≥, ≤) instead of an equal sign.

Front

How do you graph a linear inequality?

Back

1. Graph the corresponding linear equation as a boundary line. 2. Use a dashed line for < or > and a solid line for ≤ or ≥. 3. Shade the region that satisfies the inequality.

Front

What does the solution set of a linear inequality represent?

Back

The solution set represents all the points (x, y) that satisfy the inequality.

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Front

How do you find the y-intercept of a linear inequality?

Back

To find the y-intercept, set x = 0 in the inequality and solve for y.

Front

What does it mean if a point is a solution to a linear inequality?

Back

A point is a solution if it satisfies the inequality when substituted into the expression.

Front

What is the difference between a solid line and a dashed line in graphing inequalities?

Back

A solid line indicates that points on the line are included in the solution (≥ or ≤), while a dashed line indicates they are not included (> or <).

Front

How can you determine if a point is in the solution set of an inequality?

Back

Substitute the point's coordinates into the inequality. If the inequality holds true, the point is in the solution set.

Front

What is the significance of the 'rise over run' technique in graphing?

Back

The 'rise over run' technique helps determine the slope of a line, indicating how much y changes for a change in x.

Front

What does the term 'shading' refer to in graphing inequalities?

Back

Shading indicates the region of the graph that represents all the solutions to the inequality.