Slope Review

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

What is the slope formula?

Back

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

Front

Calculate the slope between the points (2, 3) and (4, 7).

Back

Using the slope formula: \( m = \frac{7 - 3}{4 - 2} = \frac{4}{2} = 2 \).

Front

Fill in the blank: Slope is known as rise over ________.

Back

run.

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

If a line has a slope of 0, what does this mean?

Back

A slope of 0 means the line is horizontal and there is no vertical change as the x-value changes.

Front

If a line has an undefined slope, what does this mean?

Back

An undefined slope means the line is vertical, and there is no horizontal change as the x-value remains constant.

Front

Calculate the slope of the line represented by the points (1, 2) and (3, 6).

Back

Using the slope formula: \( m = \frac{6 - 2}{3 - 1} = \frac{4}{2} = 2 \).

Front

What is the slope of a line that goes through the points (0, 0) and (5, 5)?

Back

The slope is \( m = \frac{5 - 0}{5 - 0} = \frac{5}{5} = 1 \).