7.7A 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 of a line represent?

Back

The slope of a line represents the rate of change of y with respect to x. It is calculated as 'rise over run'.

Front

What is the y-intercept?

Back

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

Front

How do you find the slope from two points?

Back

The slope (m) can be found using the formula m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points.

Front

What is slope-intercept form?

Back

Slope-intercept form is a way of writing linear equations as y = mx + b, where m is the slope and b is the y-intercept.

Front

What does a positive slope indicate?

Back

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

Front

What does a negative slope indicate?

Back

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

Front

How can you determine if a line is horizontal?

Back

A line is horizontal if its slope is 0, meaning there is no change in y as x changes.

Front

How can you determine if a line is vertical?

Back

A line is vertical if its slope is undefined, meaning there is no change in x as y changes.

Front

What is the formula for finding the y-intercept from a linear equation?

Back

To find the y-intercept from a linear equation in the form y = mx + b, the y-intercept is simply the value of b.