2.2 Graphing Linear Inequalities QUICK CHECK

Front

What does it mean to shade above a line in a graph of a linear inequality?

Back

It indicates that the solutions to the inequality are all the points above the line, including the line itself if the inequality is greater than or equal to (≥).

Front

What does it mean to shade below a line in a graph of a linear inequality?

Back

It indicates that the solutions to the inequality are all the points below the line, including the line itself if the inequality is less than or equal to (≤).

Front

What is the standard form of a linear inequality?

Back

The standard form of a linear inequality is typically written as Ax + By ≥ C or Ax + By ≤ C, where A, B, and C are constants.

Front

How do you determine if a point is a solution to a linear inequality?

Back

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

Front

What is the significance of the symbols > and < in linear inequalities?

Back

The symbol > indicates that the solutions are above the line, while < indicates that the solutions are below the line. Neither includes the line itself.

Front

What does the symbol ≥ indicate in a linear inequality?

Back

The symbol ≥ indicates that the solutions include all points above the line and the points on the line itself.

Front

What does the symbol ≤ indicate in a linear inequality?

Back

The symbol ≤ indicates that the solutions include all points below the line and the points on the line itself.

Front

How can you graph the inequality y < 2x + 3?

Back

First, graph the line y = 2x + 3 as a dashed line (since < does not include the line). Then shade below the line to represent all the solutions.

Front

What is the first step in writing a linear inequality from a word problem?

Back

Identify the variables and the relationship described in the problem, then translate that relationship into an inequality.

Front

In the context of the Math Pentathalon team selling drinks, how would you define the variables x and y?

Back

Let x represent the number of glasses of hot chocolate sold, and y represent the number of glasses of hot apple cider sold.