Slope

Front

What is the definition of slope?

Back

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

Front

How do you calculate the slope of a line?

Back

The slope (m) can be calculated using the formula: m = \frac{rise}{run}.

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 is the slope of a horizontal line?

Back

The slope of a horizontal line is 0, as there is no vertical change (rise) regardless of the horizontal change (run).

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined, as the run is 0 and division by zero is not possible.

Front

If a line rises 3 units for every 4 units it runs, what is the slope?

Back

The slope is \frac{3}{4}.

Front

If a line falls 2 units for every 5 units it runs, what is the slope?

Back

The slope is -\frac{2}{5}.

Front

What is the slope of the line represented by the points (2, 3) and (4, 7)?

Back

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

Front

What is the slope of the line represented by the points (1, 2) and (1, 5)?

Back

The slope is undefined because the x-coordinates are the same.