Slope - Proportional Relationships

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, usually represented as 'm'. It is calculated as the change in the y-coordinate divided by the change in the x-coordinate (rise/run).

Front

How do you find the slope between 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 a unit rate?

Back

A unit rate is a comparison of two different quantities when they are combined together. It expresses how much of one quantity corresponds to one unit of another quantity.

Front

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

Back

To find the unit rate, divide the total amount of one quantity by the total amount of the other quantity to find the value per one unit.

Front

If a car travels 120 miles in 2 hours, what is the unit rate?

Back

The unit rate is 60 miles per hour (120 miles / 2 hours).

Front

What is the slope of the line represented by the points (2, 4) and (4, 8)?

Back

The slope is m = (8 - 4) / (4 - 2) = 4 / 2 = 2.

Front

What does a slope of 0 mean?

Back

A slope of 0 means that the line is horizontal, indicating that there is no change in the y-value as the x-value changes.

Front

What does an undefined slope mean?

Back

An undefined slope occurs when a line is vertical, meaning the x-value does not change while the y-value does.