Slope Applications

Front

What does the slope of a graph represent in a real-world context?

Back

The slope represents the rate of change between two variables, indicating how one variable changes in relation to another.

Front

In the context of a graph showing gas usage, what does a slope of 1/20 mean?

Back

It means that for every mile driven, 1/20 of a gallon of gas is used.

Front

How do you calculate the average rate of change between two points on a graph?

Back

Average rate of change = (Change in y) / (Change in x).

Front

If a climber's altitude changes from 400 feet to 700 feet over 4 hours, what is the average rate of change?

Back

75 ft/h.

Front

What does the y-intercept of a graph indicate?

Back

The y-intercept indicates the starting value of the dependent variable when the independent variable is zero.

Front

In a graph showing water drainage from a pool, what does a slope of -2.4 represent?

Back

It represents that 2.4 gallons of water are drained from the pool each hour.

Front

What is the formula for calculating the slope of a line given two points (x1, y1) and (x2, y2)?

Back

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

Front

If a graph shows a constant slope, what does that imply about the relationship between the variables?

Back

It implies a linear relationship where the rate of change is consistent.

Front

What does a steeper slope indicate compared to a shallower slope?

Back

A steeper slope indicates a greater rate of change between the two variables.

Front

How can you interpret a negative slope in a real-world scenario?

Back

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