Slope from a Graph

Front

What is slope?

Back

Slope is a measure of the steepness or incline of a line, calculated 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: m = \frac{rise}{run} = \frac{y_2 - y_1}{x_2 - x_1}.

Front

What does a positive slope indicate?

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?

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 a zero slope indicate?

Back

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

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 (vertical change) and run (horizontal change), and use the slope formula.

Front

If a line rises 3 units and runs 1 unit, what is the slope?

Back

The slope is 3, calculated as \frac{3}{1}.

Front

If a line falls 5 units and runs 2 units, what is the slope?

Back

The slope is -\frac{5}{2}, indicating a negative slope.

Front

What is the slope of a line that is perfectly horizontal?

Back

The slope of a perfectly horizontal line is 0.