Graphing Linear Inequalities

Front

What is a linear inequality?

Back

A linear inequality is a mathematical statement that compares a linear expression to a value using inequality symbols (e.g., <, >, ≤, ≥).

Front

What does the graph of a linear inequality represent?

Back

The graph of a linear inequality represents all the solutions that satisfy the inequality, typically shown as a shaded region on one side of a boundary line.

Front

How do you graph a linear inequality in two variables?

Back

1. Rewrite the inequality in slope-intercept form (y = mx + b). 2. Graph the boundary line (dashed for < or >, solid for ≤ or ≥). 3. Shade the appropriate region based on the inequality.

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 that points on the line are not included (< or >).

Front

What does the inequality 3x - 2y < 10 represent graphically?

Back

It represents a region below the line 3x - 2y = 10, where all points (x, y) satisfy the inequality.

Front

How can you determine which side of the line to shade when graphing an inequality?

Back

You can test a point not on the line (commonly (0,0)). If the point satisfies the inequality, shade the side containing that point; otherwise, shade the opposite side.

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

What does the term 'slope' refer to in a linear graph?

Back

The slope refers to the steepness of the line, calculated as the rise over run (change in y over change in x).

Front

What is the y-intercept of a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, represented by the value of y when x = 0.

Front

How do you convert a linear inequality into slope-intercept form?

Back

To convert, isolate y on one side of the inequality. For example, from 3x - 2y < 10, rearrange to get y > (3/2)x - 5.