Writing equations in slope-intercept form

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.

Front

What does the slope of a line represent?

Back

The slope represents the rate of change of y with respect to x; it indicates how steep the line is.

Front

What is a positive slope?

Back

A positive slope means that as x increases, y also increases, resulting in an upward slant from left to right.

Front

What is a negative slope?

Back

A negative slope means that as x increases, y decreases, resulting in a downward slant from left to right.

Front

What does a zero slope indicate?

Back

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

Front

What does an undefined slope indicate?

Back

An undefined slope indicates a vertical line, where x does not change but y can take any value.

Front

How do you find the y-intercept from an equation?

Back

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

Front

What is the y-intercept in the equation y = 2x + 5?

Back

The y-intercept is 5.

Front

How do you calculate the slope between two points (x1, y1) and (x2, y2)?

Back

The slope (m) is calculated as m = (y2 - y1) / (x2 - x1).

Front

What is the slope of the line passing through the points (1, 2) and (3, 6)?

Back

The slope is 2, calculated as (6 - 2) / (3 - 1).