Standard Form Linear Equations

Front

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

Back

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

Front

How do you convert the standard form of a linear equation to slope-intercept form?

Back

To convert from standard form Ax + By = C to slope-intercept form, solve for y: y = -A/B * x + C/B.

Front

What are the x- and y-intercepts of a linear equation?

Back

The x-intercept is the point where the line crosses the x-axis (y=0), and the y-intercept is where it crosses the y-axis (x=0).

Front

How do you find the x-intercept of the equation 2x + 3y = 6?

Back

Set y = 0 and solve for x: 2x = 6, so x = 3. The x-intercept is (3, 0).

Front

How do you find the y-intercept of the equation 2x + 3y = 6?

Back

Set x = 0 and solve for y: 3y = 6, so y = 2. The y-intercept is (0, 2).

Front

What is the slope of the line represented by the equation 4x - 2y = 8?

Back

Rearranging to slope-intercept form gives y = 2x - 4, so the slope is 2.

Front

What does a positive slope indicate about a linear relationship?

Back

A positive slope indicates that as x increases, y also increases, showing a direct relationship.

Front

What does a negative slope indicate about a linear relationship?

Back

A negative slope indicates that as x increases, y decreases, showing an inverse relationship.

Front

How do you determine if two lines are parallel?

Back

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

Front

How do you determine if two lines are perpendicular?

Back

Two lines are perpendicular if the product of their slopes is -1.