Slope Applications

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 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

What is the y-intercept in a linear equation?

Back

The y-intercept is the point where the line crosses the y-axis, representing the value of y when x is 0.

Front

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

Back

The slope represents the rate of change between two quantities, such as speed, cost per item, or efficiency.

Front

If a pool drains 2.4 gallons of water per hour, what is the slope of the graph representing this situation?

Back

The slope is -2.4 gallons/hour, indicating a decrease in water volume.

Front

In a cost vs. weight graph, if the slope is $0.38 per ounce, what does this mean?

Back

It means that for every additional ounce of candy purchased, the cost increases by $0.38.

Front

How do you interpret the y-intercept in the context of a gas usage graph?

Back

The y-intercept indicates the initial amount of gas the tractor had before traveling any distance.

Front

What is the average rate of change and how is it calculated?

Back

The average rate of change is calculated as the change in the dependent variable divided by the change in the independent variable over a specific interval.