# Constant Rate of Change Made Easy: Lesson 1 Homework Practice Answers and Hints

## What is Constant Rate of Change and How to Calculate It: Lesson 1 Homework Practice Answers and Tricks

Constant rate of change is a concept that you may encounter in your math class or in real-life situations. It means that the ratio between two quantities that are changing is always the same. For example, if you are driving at a constant speed of 60 miles per hour, then your distance traveled and time elapsed have a constant rate of change of 60 miles per hour. In other words, for every hour that passes, you travel 60 miles.

## lesson 1 homework practice constant rate of change answers

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Constant rate of change is also related to the idea of proportionality. Two quantities are proportional if they have a constant rate of change. For example, if you buy apples at $2 per pound, then the cost of apples and the weight of apples are proportional, with a constant rate of change of $2 per pound. In other words, for every pound of apples that you buy, you pay $2.

In this article, we will show you how to find the constant rate of change from different representations, such as tables, graphs, equations, and word problems. We will also give you some tips and tricks to solve these problems easily and accurately.

## How to Find the Constant Rate of Change from Tables

A table is a way of organizing data that shows how two quantities change in relation to each other. To find the constant rate of change from a table, you need to look at how much one quantity changes when the other quantity changes by a certain amount. This is also called the slope or the unit rate.

For example, look at this table that shows the distance traveled by a car and the time elapsed:

Time (hours)Distance (miles)

00

150

2100

3150

4200

To find the constant rate of change from this table, we need to pick any two rows and see how much the distance changes when the time changes by one hour. For example, we can pick the first and second rows and see that when the time changes from 0 to 1 hour, the distance changes from 0 to 50 miles. This means that the constant rate of change is 50 miles per hour.

We can also pick any other two rows and get the same result. For example, we can pick the third and fourth rows and see that when the time changes from 2 to 3 hours, the distance changes from 100 to 150 miles. This also means that the constant rate of change is 50 miles per hour.

If the table has a constant rate of change, then we should get the same result no matter which two rows we pick. If we get different results, then the table does not have a constant rate of change.

## How to Find the Constant Rate of Change from Graphs

A graph is a way of visualizing data that shows how two quantities change in relation to each other. To find the constant rate of change from a graph, you need to look at how steep or flat the graph is. This is also called the slope or the unit rate.

For example, look at this graph that shows the distance traveled by a car and the time elapsed:

To find the constant rate of change from this graph, we need to pick any two points on the line and see how much the distance changes when the time changes by a certain amount. This is also called finding the rise over run. For example, we can pick the points (0,0) and (1,50) and see that when the time changes from 0 to 1 hour, the distance changes from 0 to 50 miles. This means that the constant rate of change is

## How to Find the Constant Rate of Change from Equations

An equation is a way of expressing a relationship between two quantities using symbols and operations. To find the constant rate of change from an equation, you need to look at the coefficient of the independent variable. This is also called the slope or the unit rate.

For example, look at this equation that shows the distance traveled by a car and the time elapsed:

d = 50t + 10

To find the constant rate of change from this equation, we need to look at the coefficient of t, which is 50. This means that the constant rate of change is 50 miles per hour. In other words, for every hour that passes, the distance increases by 50 miles.

If the equation has a constant rate of change, then it should be in the form y = mx + b, where m is the slope and b is the y-intercept. If the equation is not in this form, then it does not have a constant rate of change.

## How to Find the Constant Rate of Change from Word Problems

A word problem is a way of describing a situation using words and numbers. To find the constant rate of change from a word problem, you need to identify the two quantities that are changing and how they are related. Then, you need to use the formula (y2y1)/(x2x1) ( y 2 y 1) / ( x 2 x 1) to calculate the rate of change.

For example, look at this word problem that shows the distance traveled by a car and the time elapsed:

A car travels at a constant speed of 50 miles per hour for 4 hours. How far does it travel?

To find the constant rate of change from this word problem, we need to identify the two quantities that are changing and how they are related. The two quantities are distance and time, and they are related by the equation d = 50t. Then, we need to use the formula (y2y1)/(x2x1) ( y 2 y 1) / ( x 2 x 1) to calculate the rate of change. We can use any two points that satisfy the equation, such as (0,0) and (4,200). Then, we get:

(y2y1)/(x2x1) = (2000)/(40) = 200/4 = 50

This means that the constant rate of change is 50 miles per hour.

## How to Find the Constant Rate of Change from Verbal Descriptions

A verbal description is a way of describing a situation using words and numbers. To find the constant rate of change from a verbal description, you need to identify the two quantities that are changing and how they are related. Then, you need to use the formula (y2y1)/(x2x1) ( y 2 y 1) / ( x 2 x 1) to calculate the rate of change.

For example, look at this verbal description that shows the distance traveled by a car and the time elapsed:

A car travels at a constant speed of 40 miles per hour for 3 hours. How far does it travel?

To find the constant rate of change from this verbal description, we need to identify the two quantities that are changing and how they are related. The two quantities are distance and time, and they are related by the equation d = 40t. Then, we need to use the formula (y2y1)/(x2x1) ( y 2 y 1) / ( x 2 x 1) to calculate the rate of change. We can use any two points that satisfy the equation, such as (0,0) and (3,120). Then, we get:

(y2y1)/(x2x1) = (1200)/(30) = 120/3 = 40

This means that the constant rate of change is 40 miles per hour.

## How to Use the Constant Rate of Change to Make Predictions

One of the applications of the constant rate of change is to make predictions based on a linear model. If we know the initial value and the rate of change of a function, we can use them to estimate the output value for any given input value. We can also use them to estimate the input value for any given output value.

For example, suppose we know that a car rental company charges $25 per day plus $0.15 per mile for renting a car. We can use this information to find the initial value and the rate of change of a function that models the total cost of renting a car for a certain number of days and miles. Let C be the total cost in dollars and let d be the number of days and m be the number of miles. Then we have:

Initial Value: The cost when both d and m are zero is $25, so $25 is the initial value for C.

Rate of Change: The cost increases by $25 for each day and by $0.15 for each mile, so $25 per day and $0.15 per mile are the rates of change for C.

Using these values, we can write a formula for C in terms of d and m:

C = 25d + 0.15m + 25

This formula allows us to make predictions based on different values of d and m. For example, if we want to rent a car for 5 days and drive 200 miles, we can plug in d = 5 and m = 200 and get:

C = 25(5) + 0.15(200) + 25

C = 125 + 30 + 25

C = 180

This means that renting a car for 5 days and driving 200 miles would cost $180.

## How to Find the Constant Rate of Change from Graphs and Tables

A graph is a way of visualizing data that shows how two quantities change in relation to each other. A table is a way of organizing data that shows how two quantities change in relation to each other. To find the constant rate of change from a graph or a table, you need to look at how much one quantity changes when the other quantity changes by a certain amount. This is also called the slope or the unit rate.

For example, look at this graph and table that show the distance traveled by a car and the time elapsed:

Time (hours)Distance (miles)

00

150

2100

3150

4200

To find the constant rate of change from this graph or table, we need to pick any two points on the line or any two rows in the table and see how much the distance changes when the time changes by one hour. This is also called finding the rise over run. For example, we can pick the points (0,0) and (1,50) or the first and second rows and see that when the time changes from 0 to 1 hour, the distance changes from 0 to 50 miles. This means that the constant rate of change is 50 miles per hour.

We can also pick any other two points or rows and get the same result. For example, we can pick the points (2,100) and (3,150) or the third and fourth rows and see that when the time changes from 2 to 3 hours, the distance changes from 100 to 150 miles. This also means that the constant rate of change is 50 miles per hour.

If the graph is a straight line or the table has a constant difference between consecutive values, then they have a constant rate of change. If we get different results for different points or rows, then they do not have a constant rate of change.

## How to Use the Constant Rate of Change to Write Equations

One of the applications of the constant rate of change is to write equations that represent linear functions. If we know the initial value and the rate of change of a function, we can use them to write an equation in slope-intercept form: y = mx + b, where m is the slope and b is the y-intercept.

For example, suppose we know that a car rental company charges $25 per day plus $0.15 per mile for renting a car. We can use this information to find the initial value and the rate of change of a function that models the total cost of renting a car for a certain number of days and miles. Let C be the total cost in dollars and let d be the number of days and m be the number of miles. Then we have:

Initial Value: The cost when both d and m are zero is $25, so $25 is the initial value for C.

Rate of Change: The cost increases by $25 for each day and by $0.15 for each mile, so $25 per day and $0.15 per mile are the rates of change for C.

Using these values, we can write an equation for C in terms of d and m:

C = 25d + 0.15m + 25

This equation allows us to calculate the total cost for any given values of d and m.

## Conclusion

In this article, we have learned how to find the constant rate of change of a function from different representations, such as equations, graphs, tables, word problems, and verbal descriptions. We have also learned how to use the constant rate of change to make predictions and write equations for linear functions. The constant rate of change is a useful concept that helps us understand and model many real-world situations that involve quantities with a constant ratio. b99f773239

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