Unit rate and slope

Front

What is the definition of unit rate?

Back

A unit rate is a ratio that compares a quantity to one unit of another quantity, often expressed as 'x per 1 unit'.

Front

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

Back

To calculate the unit rate, divide the total quantity by the number of units. For example, if you travel 120 miles in 2 hours, the unit rate is 120 miles ÷ 2 hours = 60 miles per hour.

Front

What is the definition of slope in a graph?

Back

Slope is a measure of the steepness of a line on a graph, 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 from two points on a graph?

Back

Use the formula: slope (m) = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are the coordinates of the two points.

Front

What does a slope of 0 indicate about a line on a graph?

Back

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

Front

What does a positive slope indicate about a relationship between two variables?

Back

A positive slope indicates that as one variable increases, the other variable also increases.

Front

What does a negative slope indicate about a relationship between two variables?

Back

A negative slope indicates that as one variable increases, the other variable decreases.

Front

If a graph shows a rate of change of 40, what does this mean?

Back

It means that for every unit increase in the x-variable, the y-variable increases by 40 units.

Front

How can you interpret the unit rate in a real-world context?

Back

The unit rate can be used to compare different quantities, such as speed (miles per hour) or cost (dollars per item), making it easier to understand and make decisions.

Front

What is the significance of the scale on a graph when determining rate of change?

Back

The scale on a graph affects how steep the line appears and is crucial for accurately calculating the rate of change.