Slopes from a Graph

Front

What is the definition of slope?

Back

Slope is a measure of the steepness or incline of a line, typically represented as the ratio of the vertical change (rise) to the horizontal change (run) between two points on the line.

Front

What is the formula for calculating slope?

Back

The formula for slope (m) is given by: m = \frac{y_2 - y_1}{x_2 - x_1}, where (x_1, y_1) and (x_2, y_2) are two points on the line.

Front

What does a positive slope indicate about a line?

Back

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

Front

What does an undefined slope indicate?

Back

An undefined slope indicates a vertical line, where the x-values are constant and the line does not rise or fall.

Front

What does a slope of zero indicate?

Back

A slope of zero indicates a horizontal line, where the y-values are constant and the line does not rise or fall.

Front

How do you find the slope from a graph?

Back

To find the slope from a graph, select two points on the line, determine the rise (change in y) and run (change in x), and apply the slope formula.

Front

If a line goes through the points (2, 3) and (5, 7), what is the slope?

Back

The slope is m = \frac{7 - 3}{5 - 2} = \frac{4}{3}.

Front

What is the slope of a line that is vertical?

Back

The slope of a vertical line is undefined.

Front

What is the slope of a line that is horizontal?

Back

The slope of a horizontal line is 0.