Slope: Rise over Run

Front

What is the definition of slope in mathematics?

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 does 'rise over run' mean in the context of slope?

Back

'Rise over run' refers to the formula used to calculate the slope of a line, where 'rise' is the change in the y-coordinates and 'run' is the change in the x-coordinates between two points.

Front

What is the slope of a horizontal line?

Back

The slope of a horizontal line is 0.

Front

What is the slope of a vertical line?

Back

The slope of a vertical line is undefined.

Front

Calculate the slope between the points (2, 3) and (5, 7).

Back

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

Front

If a line has a slope of 1, what does this indicate about the line?

Back

A slope of 1 indicates that for every unit increase in x, there is a corresponding unit increase in y, resulting in a 45-degree angle with the x-axis.

Front

What is the slope of the line represented by the equation y = 2x + 1?

Back

The slope of the line is 2.

Front

Find the slope of the line passing through the points (1, 2) and (3, 6).

Back

The slope is \( \frac{6 - 2}{3 - 1} = \frac{4}{2} = 2 \).

Front

What is the slope of the line represented by the equation y = -3x + 4?

Back

The slope of the line is -3.

Front

If the slope of a line is negative, what does this indicate about the direction of the line?

Back

A negative slope indicates that the line is decreasing, meaning as x increases, y decreases.