Rate of Change and Initial Value

Front

What is the rate of change?

Back

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

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

Front

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

Back

To calculate the rate of change from a graph, find two points on the line, determine the change in the y-values (rise) and the change in the x-values (run), and then divide the rise by the run.

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

Front

What is the initial value in a linear equation?

Back

The initial value is the starting point of a function or relationship, often represented as the y-intercept in a linear equation.

Tags

CCSS.HSF-IF.C.7A

Front

In the equation y = mx + b, what does 'b' represent?

Back

'b' represents the initial value or y-intercept of the line, which is the value of y when x is 0.

Tags

CCSS.8.EE.B.6

CCSS.8.F.A.3

Front

If a car club charges a $30 join up fee and $5 monthly, what is the initial value?

Back

The initial value is $30, which is the one-time fee to join the club.

Tags

CCSS.HSF.LE.B.5

Front

What does a positive rate of change indicate?

Back

A positive rate of change indicates that as one quantity increases, the other quantity also increases.

Tags

CCSS.HSF-LE.A.1B

Front

What does a negative rate of change indicate?

Back

A negative rate of change indicates that as one quantity increases, the other quantity decreases.

Tags

CCSS.HSF-LE.A.1B

Front

How can you represent a rate of change in a real-world scenario?

Back

A rate of change can be represented by the speed of a car (miles per hour) or the cost of a subscription service (dollars per month).

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

Front

What is the formula for calculating the rate of change?

Back

Rate of Change = (Change in y) / (Change in x) or (y2 - y1) / (x2 - x1).

Tags

CCSS.8.F.B.4

CCSS.HSF.IF.B.6

Front

If Tim pays $125 for a phone and $50 monthly, what is the total cost after 3 months?

Back

Total cost = $125 + (3 * $50) = $125 + $150 = $275.

Tags

CCSS.6.EE.B.6