Rate of Change & Word Problems

Front

What is the rate of change in a linear equation?

Back

The rate of change in a linear equation represents how much the dependent variable (y) changes for a unit change in the independent variable (x). It is often represented by the slope (m) in the equation y = mx + b.

Tags

CCSS.HSF-LE.A.1B

Front

Define y-intercept.

Back

The y-intercept is the point where a line crosses the y-axis. It is the value of y when x is 0.

Front

Write the equation for a service charge of $25 plus $50 per hour.

Back

y = 50x + 25, where y is the total charge and x is the number of hours.

Tags

CCSS.8.F.B.4

CCSS.HSF.LE.A.2

Front

What does a constant rate of change indicate?

Back

A constant rate of change indicates that the relationship between the variables is linear, meaning that for every unit increase in x, y increases by a fixed amount.

Tags

CCSS.HSF-LE.A.1B

Front

How do you find the constant rate of change from a graph?

Back

To find the constant rate of change from a graph, calculate the slope by taking the change in y (vertical change) divided by the change in x (horizontal change) between two points on the line.

Tags

CCSS.HSF-LE.A.1B

Front

What is the formula for calculating slope?

Back

The formula for calculating slope (m) is m = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on the line.

Tags

CCSS.8.EE.B.5

Front

If a panda weighs 2 lbs at birth, what can you conclude about its weight compared to another panda of the same weight?

Back

If both pandas weigh 2 lbs at birth, they have the same weight.

Front

What is the significance of the slope in a real-world context?

Back

In a real-world context, the slope represents the rate at which one quantity changes in relation to another, such as speed, cost per hour, or growth rate.

Tags

CCSS.8.EE.B.5

Front

How can you interpret a negative slope in a word problem?

Back

A negative slope indicates that as one variable increases, the other variable decreases, showing an inverse relationship.

Tags

CCSS.8.EE.B.5

Front

What does it mean if the rate of change is $41 per month?

Back

It means that for every month that passes, the quantity being measured increases by $41.

Tags

CCSS.HSF-LE.A.1B