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.

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.

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.

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.

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.

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.

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.

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.