Slope - Proportional Relationships

Front

What is the definition of slope in the context of proportional relationships?

Back

Slope is a measure of the rate of change between two variables, typically represented as the ratio of the change in the vertical direction (rise) to the change in the horizontal direction (run).

Front

How do you calculate the slope from a table of values?

Back

To calculate the slope from a table, select two points (x1, y1) and (x2, y2) and use the formula: slope = (y2 - y1) / (x2 - x1).

Front

What does a slope of 45 miles per hour indicate?

Back

A slope of 45 miles per hour indicates that for every hour, the distance traveled is 45 miles.

Front

What is the significance of a slope of 40 in a graph?

Back

A slope of 40 indicates that for every unit increase in the independent variable, the dependent variable increases by 40 units.

Front

What does the phrase '2 boys for every 1 girl' represent in terms of slope?

Back

This phrase represents a rate of change or slope, indicating that for every 1 girl, there are 2 boys, which can be expressed as a ratio of 2:1.

Front

How can you determine if a graph is proportional?

Back

A graph is proportional if it passes through the origin (0,0) and has a constant slope.

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 of one variable by the total quantity of the other variable, ensuring the denominator is 1.

Front

What is the relationship between slope and unit rate in proportional relationships?

Back

In proportional relationships, the slope of the line represents the unit rate, indicating how much one variable changes in relation to another.

Front

What is the formula for calculating slope from a graph?

Back

The formula for calculating slope from a graph is: slope = (change in y) / (change in x).