Slope and Proportional Relationships

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 using two points (x1, y1) and (x2, y2)?

Back

The slope (m) is calculated using the formula: m = (y2 - y1) / (x2 - x1).

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 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 horizontal change (run) is 0, leading to division by zero.

Front

What is a unit rate?

Back

A unit rate is a comparison of two different quantities when they are combined together, expressed as a quantity per one unit of another quantity.

Front

How do you find the unit rate from a proportional relationship?

Back

To find the unit rate, divide the total quantity by the number of units. For example, if a car travels 120 miles in 2 hours, the unit rate is 120 miles / 2 hours = 60 miles per hour.

Front

What is the rise/run method for finding slope?

Back

The rise/run method involves counting the vertical change (rise) and the horizontal change (run) between two points on a graph to determine the slope.

Front

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

Back

Using the formula m = (y2 - y1) / (x2 - x1), the slope is m = (7 - 3) / (5 - 2) = 4/3.