A.3B Rate of Change

Front

What is the rate of change in a linear function?

Back

The rate of change in a linear function is the ratio of the change in the y-value to the change in the x-value, often represented as the slope (m) of the line.

Front

How do you calculate the average rate of change of a function?

Back

The average rate of change of a function between two points (x1, y1) and (x2, y2) is calculated using the formula: \( \text{Average Rate of Change} = \frac{y_2 - y_1}{x_2 - x_1} \)

Front

What does a negative rate of change indicate?

Back

A negative rate of change indicates that as the x-value increases, the y-value decreases, showing a downward trend in the graph.

Front

What is the slope of the line represented by the equation 2x - 3y = 6?

Back

To find the slope, rearrange the equation to slope-intercept form (y = mx + b): \( y = \frac{2}{3}x - 2 \). The slope (m) is \( \frac{2}{3} \).

Front

If a tree grows from 4.5 feet to 15.75 feet in 5 years, what is the rate of growth?

Back

The rate of growth is calculated as: \( \frac{15.75 - 4.5}{5} = 2.25 \) feet per year.

Front

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

Back

The formula for the slope (m) is: \( m = \frac{y_2 - y_1}{x_2 - x_1} \)

Front

What does the term 'rate of change' refer to in mathematics?

Back

The rate of change refers to how much a quantity changes in relation to the change in another quantity, often expressed as a ratio.

Front

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

Back

To determine the rate of change from a graph, select two points on the line, find their coordinates, and apply the slope formula: \( m = \frac{y_2 - y_1}{x_2 - x_1} \)

Front

What is the average rate of change of the area of a circle as the radius increases from 2.5 to 5.5 feet?

Back

The average rate of change is \( 25.12 \) square feet per foot.

Front

What is the significance of the slope in a linear function?

Back

The slope indicates the steepness of the line and the direction of the relationship between the variables; a positive slope indicates an increasing relationship, while a negative slope indicates a decreasing relationship.