Slope - Proportional Relationships

Front

What is slope in the context of a graph?

Back

Slope is a measure of the steepness or incline of a line, calculated as the change in the vertical direction (rise) divided by the change in the horizontal direction (run).

Front

How do you calculate the slope from two points (x1, y1) and (x2, y2)?

Back

Slope (m) = (y2 - y1) / (x2 - x1).

Front

What does a positive slope indicate about a line on a graph?

Back

A positive slope indicates that as the x-value increases, the y-value also increases, showing a direct relationship.

Front

What does a negative slope indicate about a line on a graph?

Back

A negative slope indicates that as the x-value increases, the y-value decreases, showing an inverse relationship.

Front

What is a slope of zero?

Back

A slope of zero indicates a horizontal line, meaning there is no change in the y-value as the x-value changes.

Front

What is an undefined slope?

Back

An undefined slope occurs with a vertical line, where the x-value does not change, leading to division by zero.

Front

In a proportional relationship, how is slope represented?

Back

In a proportional relationship, the slope is constant and represents the ratio of the change in y to the change in x.

Front

If a car travels 90 miles in 2 hours, what is the slope (speed) in miles per hour?

Back

Slope = 90 miles / 2 hours = 45 miles per hour.

Front

If you earn $54 in 6 hours, what is your hourly rate (slope)?

Back

Hourly rate = $54 / 6 hours = $9 per hour.

Front

What is the slope of a graph that shows distance traveled over gallons of gasoline used?

Back

The slope represents the miles per gallon, indicating fuel efficiency.