Rate of Change

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form is given by the equation y = mx + b, where m is the slope and b is the y-intercept.

Front

What does the slope of a line represent?

Back

The slope represents the rate of change of y with respect to x. It indicates how much y changes for a unit change in x.

Front

How do you calculate the slope between two points (x1, y1) and (x2, y2)?

Back

The slope (m) is calculated using the formula m = (y2 - y1) / (x2 - x1).

Front

What is the rate of change of a function?

Back

The rate of change of a function describes how the output value (y) changes as the input value (x) changes.

Front

If a tree grows 7 feet in 1 year, what is the rate of change of its height?

Back

The rate of change is 7 ft/yr.

Front

What is the meaning of a negative slope?

Back

A negative slope indicates that as x increases, y decreases. It represents a decrease in the value of y.

Front

What is the meaning of a positive slope?

Back

A positive slope indicates that as x increases, y also increases. It represents a growth in the value of y.

Front

Find the slope of the line that passes through the points (2, 4) and (6, 12).

Back

The slope is 2.

Front

What is the rate of change of y with respect to x if y = -rac{3}{4}x + 5?

Back

The rate of change is -rac{3}{4}.

Front

What is the slope of the line represented by the equation y = 2x + 3?

Back

The slope is 2.