Graphing Linear Inequalities

Front

What is a linear inequality?

Back

A linear inequality is a mathematical statement that relates a linear expression to a value using inequality symbols (>, <, ≥, ≤) instead of an equal sign.

Front

What does the slope of a line represent?

Back

The slope of a line represents the rate of change of the y-coordinate with respect to the x-coordinate. It indicates how steep the line is.

Front

How do you determine the slope from two points (x1, y1) and (x2, y2)?

Back

Front

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

Back

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 graph a linear inequality?

Back

1. Graph the corresponding linear equation as a line. 2. Use a solid or dashed line based on the inequality. 3. Shade the region that satisfies the inequality.

Front

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

Back

Shading a region indicates all the solutions to the inequality. The shaded area represents all the points (x, y) that satisfy the inequality.

Front

What is the y-intercept of a line?

Back

Front

How can you find the x-intercept of a line?

Back

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

Front

What is the significance of the slope in real-world applications?

Back

The slope can represent rates of change, such as speed, cost per item, or growth rates, making it useful in various real-world contexts.