Greater Rate of Change

Front

What is the rate of change in mathematics?

Back

The rate of change is a measure of how much a quantity changes in relation to another quantity, often expressed as a ratio or a slope.

Front

How do you determine the rate of change from a graph?

Back

The rate of change can be determined by calculating the slope of the line, which is the rise (change in y) over the run (change in x).

Front

What does a greater rate of change indicate about a function?

Back

A greater rate of change indicates that the function is increasing or decreasing more rapidly.

Front

What is a y-intercept?

Back

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

Front

How can you find the y-intercept from an equation?

Back

To find the y-intercept from an equation in the form y = mx + b, the y-intercept is the value of b.

Front

What does it mean if two lines have the same y-intercept?

Back

If two lines have the same y-intercept, they cross the y-axis at the same point, but they may have different slopes.

Front

What is the significance of comparing rates of change between two functions?

Back

Comparing rates of change helps to understand which function is increasing or decreasing faster, which is important in real-world applications.

Front

How do you compare the rates of change of two linear functions?

Back

To compare the rates of change of two linear functions, compare their slopes; the function with the larger slope has the greater rate of change.

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line, defined by the equation y = mx + b, where m is the slope and b is the y-intercept.

Front

What does a negative rate of change indicate?

Back

A negative rate of change indicates that the function is decreasing as the input increases.