Graphing Linear Equations

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 does the slope (m) represent in a linear equation?

Back

The slope (m) represents the rate of change of y with respect to x. It indicates how steep the line is and the direction it goes (positive slope goes up, negative slope goes down).

Front

What is the y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis. It is represented as (0, b) in the equation y = mx + b.

Front

How do you find the y-intercept from the equation y = -2x + 5?

Back

Set x = 0. The y-intercept is (0, 5).

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 determine if two lines are parallel?

Back

Two lines are parallel if they have the same slope (m) but different y-intercepts (b).

Front

What does it mean if a linear equation has a slope of 0?

Back

A slope of 0 means the line is horizontal, indicating that y does not change as x changes.

Front

What is the slope of the line represented by the equation y = 4?

Back

The slope is 0, as the line is horizontal.

Front

How do you graph the equation y = 3x - 2?

Back

Start at the y-intercept (0, -2), then use the slope (3) to rise 3 units up and run 1 unit to the right to find another point.

Front

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

Back

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.