Linear Equations

Front

What is the slope of a line represented by the equation 4x - 6y = 12?

Back

The slope is 2/3.

Front

Define 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 term 'slope' refer to in a linear equation?

Back

The slope refers to the steepness of the line, calculated as the rise over run (change in y over change in x).

Front

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

Back

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

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

Convert the equation 2x + 3y = 6 to slope-intercept form.

Back

The slope-intercept form is y = -2/3x + 2.

Front

What is the significance of the y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, indicating the value of y when x = 0.

Front

If a line has a slope of 0, what does that indicate about the line?

Back

A slope of 0 indicates a horizontal line, meaning there is no change in y as x changes.

Front

What does it mean if a line has an undefined slope?

Back

An undefined slope indicates a vertical line, where x remains constant regardless of the value of y.

Front

How can you determine if two lines are parallel?

Back

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