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

What does it mean when a graph is shaded above the line?

Back

It indicates that the solutions to the inequality are all the points above the line, meaning the y-values are greater than the values on the line.

Front

What does it mean when a graph is shaded below the line?

Back

It indicates that the solutions to the inequality are all the points below the line, meaning the y-values are less than the values on the line.

Front

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

Back

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

Front

How do you determine 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, then the point is a solution.

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 graph the inequality y > 2x + 1?

Back

Graph the line y = 2x + 1 with a dotted line, then shade above the line.

Front

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

Back

It represents a line with a slope of 3 and a y-intercept of -2, with the area below and including the line shaded.

Front

What is the first step in graphing the inequality 3x - 2y < 10?

Back

Rearrange the inequality into slope-intercept form (y > mx + b) to identify the line and shading direction.

Front

What does the term 'solution set' refer to in the context of inequalities?

Back

The solution set is the collection of all points (x, y) that satisfy the inequality.