Graphing Linear Equations and Inequalities Practice

Front

What is a linear equation?

Back

A linear equation is an equation that makes a straight line when graphed. It can be written in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, usually represented by the letter m. It is calculated as the change in y divided by the change in x (rise/run).

Front

What does the y-intercept represent in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis. It is represented by the value of b in the equation y = mx + b.

Front

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

Back

To determine if an ordered pair (x, y) is a solution to an inequality, substitute x and y into the inequality. If the inequality holds true, then the ordered pair is a solution.

Front

What is the difference between a linear equation and a linear inequality?

Back

A linear equation shows equality (e.g., y = 2x + 3), while a linear inequality shows a range of values (e.g., y < 2x + 3) and is represented by a shaded region on a graph.

Front

What does it mean for a point to be above a line in a graph of an inequality?

Back

If a point is above a line in a graph of an inequality, it means that the y-value of the point is greater than the y-value of the line at that x-value, satisfying the inequality.

Front

What is the standard form of a linear equation?

Back

The standard form of a linear equation is Ax + By = C, where A, B, and C are integers, and A should be non-negative.

Front

How can you graph a linear equation?

Back

To graph a linear equation, find at least two points that satisfy the equation, plot them on a coordinate plane, and draw a straight line through the points.

Front

What does it mean for a line to be horizontal?

Back

A horizontal line has a slope of 0 and can be represented by the equation y = b, where b is the y-value for all x-values.

Front

What does it mean for a line to be vertical?

Back

A vertical line has an undefined slope and can be represented by the equation x = a, where a is the x-value for all y-values.