Question

List two similarities between graphing two-variable inequalities like x + y > 10 and graphing one-variable inequalities, such as x < 5. What are the similarities?

A) Both involve plotting points on a graph.
B) Both involve shading regions on the graph.
C) Both involve solving for a single variable.
D) Both involve linear equations.

Answer 1

Both graphing two-variable inequalities and one-variable inequalities involve shading regions and plotting points to determine boundaries, with shading indicating the solution set. Two-variable inequalities create boundary lines on a graph, while one-variable inequalities mark a single point on a number line.

Step-by-step explanation:

The similarities between graphing two-variable inequalities like x + y > 10 and graphing one-variable inequalities such as x < 5 include:

• B) Both involve shading regions on the graph.
• A) Both involve plotting points on a graph.

When graphing an inequality, whether it is a one-variable or two-variable inequality, part of the solution process involves identifying a region on the coordinate plane or number line that satisfies the inequality. This is indicated by shading that region. Additionally, both types of inequalities can involve plotting points to determine the boundary of the shaded area. However, unlike two-variable inequalities which create boundary lines, one-variable inequalities mark a single point on the number line as the boundary.