Bear - Finding Rate of Change from a Graph

Front

What is the definition of slope in a graph?

Back

The slope of a line is a measure of its steepness, calculated as the ratio of the vertical change (rise) to the horizontal change (run) between two points on the line.

Front

How do you find the slope of a line given two points (x1, y1) and (x2, y2)?

Back

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

Front

What does an undefined slope indicate about a line?

Back

An undefined slope indicates a vertical line, where the change in x is zero, leading to division by zero.

Front

What does a slope of 0 indicate about a line?

Back

A slope of 0 indicates a horizontal line, where there is no vertical change as x changes.

Front

What is the rate of change in a graph?

Back

The rate of change is the ratio of the change in the dependent variable to the change in the independent variable, often represented as the slope of the line.

Front

If a car travels 128 miles using 4 gallons of gasoline, what is the rate of change in miles per gallon?

Back

Rate of change = 128 miles / 4 gallons = 32 miles per gallon.

Front

How can you interpret the slope of a line in a real-world context?

Back

The slope can represent a rate, such as speed (miles per hour) or cost per item (dollars per item), depending on the variables plotted on the axes.

Front

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

Back

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

Front

In the context of a graph showing rainfall over time, how would you interpret a slope of 2 cm per hour?

Back

This means that the rainfall increases by 2 centimeters for every hour that passes.