Slope / Slope-intercept form

Front

What is the definition of slope?

Back

Slope is defined as the ratio of the rise (change in y) to the run (change in x) between two points on a line.

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

Back

The slope (m) is calculated using the formula: m = (y2 - y1) / (x2 - x1).

Front

What does a positive slope indicate about a line?

Back

A positive slope indicates that as x increases, y also increases, meaning the line rises from left to right.

Front

What does a negative slope indicate about a line?

Back

A negative slope indicates that as x increases, y decreases, meaning the line falls from left to right.

Front

What does a zero slope indicate about a line?

Back

A zero slope indicates a horizontal line, where y remains constant as x changes.

Front

What does an undefined slope indicate?

Back

An undefined slope indicates a vertical line, where x remains constant as y changes.

Front

If the slope of a line is 3, what does this mean in terms of rise and run?

Back

A slope of 3 means that for every 1 unit of run (horizontal change), there is a rise of 3 units (vertical change).

Front

Find the slope of the line passing through the points (2, 3) and (4, 7).

Back

The slope is m = (7 - 3) / (4 - 2) = 4 / 2 = 2.

Front

Find the slope of the line passing through the points (1, 2) and (3, 8).

Back

The slope is m = (8 - 2) / (3 - 1) = 6 / 2 = 3.