TEKS 10.3D: 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 (>, <, ≥, ≤). It represents a region of the coordinate plane.

Front

What does the symbol '>' indicate in a linear inequality?

Back

The symbol '>' indicates that the expression on the left is greater than the expression on the right, meaning the solutions are above the line when graphed.

Front

What does the symbol '≥' indicate in a linear inequality?

Back

The symbol '≥' indicates that the expression on the left is greater than or equal to the expression on the right, meaning the solutions include the line and the area above it when graphed.

Front

How do you graph a linear inequality?

Back

1. Graph the corresponding linear equation as a dashed line (for < or >) or solid line (for ≤ or ≥). 2. Shade the region that represents the solutions.

Front

Back

The solution set includes all ordered pairs (x, y) that satisfy the inequality, such as (-3, 5).

Front

How do you determine if an ordered pair is a solution to a linear inequality?

Back

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

Front

What is the slope-intercept form of a linear equation?

Back

Front

What does the slope of a line represent in a linear inequality?

Back

The slope represents the rate of change of y with respect to x. It indicates how steep the line is and the direction it goes.

Front

Back

The y-intercept is -4, which is the point where the line crosses the y-axis.

Front

How do you find the x-intercept of a linear equation?

Back

To find the x-intercept, set y = 0 in the equation and solve for x.