Unit Rate as Slope

Front

What is a unit rate?

Back

A unit rate is a ratio that compares a quantity to one unit of another quantity, often expressed as 'per' something, like miles per hour or dollars per item.

Front

How do you calculate the slope of a line?

Back

The slope of a line is calculated by taking the change in the y-values (rise) divided by the change in the x-values (run) between two points on the line.

Front

If Mrs. Soto can decorate 5 cupcakes in 2 minutes, what is her unit rate in cupcakes per minute?

Back

Her unit rate is 2.5 cupcakes per minute (5 cupcakes ÷ 2 minutes).

Front

What does a slope of 1 represent in a graph?

Back

A slope of 1 means that for every 1 unit increase in the x-direction, there is a 1 unit increase in the y-direction, indicating a direct proportional relationship.

Front

If Leslie paid $12 for 2 shirts, what is the unit rate per shirt?

Back

The unit rate is $6 per shirt ($12 ÷ 2 shirts).

Front

What does a negative slope indicate in a graph?

Back

A negative slope indicates that as one variable increases, the other variable decreases, showing an inverse relationship.

Front

If Jose rode his bike 9 miles in 30 minutes, what is his speed in miles per hour?

Back

His speed is 18 miles per hour (9 miles ÷ 0.5 hours).

Front

What is the significance of the slope in a real-world context?

Back

The slope can represent rates of change, such as speed, cost per item, or any other ratio that describes how one quantity changes in relation to another.

Front

If a scuba diver descends at a rate of 15 ft per minute, what does this rate tell us?

Back

This rate indicates that for every minute that passes, the diver goes down 15 feet.

Front

How can you represent a unit rate on a graph?

Back

A unit rate can be represented as the slope of a line on a graph, where the x-axis represents one quantity and the y-axis represents the other.