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 (>, <, ≥, ≤).

Front

How do you graph a linear inequality?

Back

To graph a linear inequality, first graph the corresponding linear equation as a dashed line (for < or >) or a solid line (for ≤ or ≥). Then, shade the region that satisfies the inequality.

Front

What does the shaded area in a graph of a linear inequality represent?

Back

The shaded area represents all the solutions to the inequality, indicating where the values of x and y satisfy the inequality.

Front

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

Back

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

Front

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

Back

You can test a point not on the line (often (0,0) if it's not on the line) to see if it satisfies the inequality. If it does, shade the side containing that point.

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 convert a linear inequality into slope-intercept form?

Back

To convert a linear inequality into slope-intercept form, isolate y on one side of the inequality.

Front

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

Back

It represents a region below the line y = 2x + 3, with a dashed line indicating that points on the line are not included.

Front

What is the significance of the y-intercept in a linear inequality?

Back

The y-intercept is the point where the line crosses the y-axis, providing a starting point for graphing the inequality.

Front

How can you check if a point is a solution to a linear inequality?

Back

Substitute the x and y values of the point into the inequality. If the inequality holds true, the point is a solution.