Constant Rate of Change Notes

Presentation

•

Mathematics

•

8th Grade

•

Hard

Joseph Anderson

FREE Resource

14 Slides • 15 Questions

Rate of Change

I can identify the rate of change.

Criteria for Success

Accurately identify the rate of change in a table
Accurately identify the rate of change in a equation
Accurately identify the rate of change in a verbal problem

Vocabulary

Rate of Change

A rate of change is a rate that describes how one quantity changes in relation to another quantity.
If x is the independent variable and y is the dependent variable, then:

rate\ of\ change\ =\frac{\Delta y}{\Delta x}\ \ ,\ \Delta\ means\ change

Warm up!

Table

We learned about rate of change in tables already, so let us start there :)

Multiple Choice

What is the constant rate of change?

Not here.

$80 per month.

$82 per month.

$41 per month.

Multiple Choice

What is the rate of change for this table?

1/9

1/8

Multiple Choice

What is the constant rate of change between the quantities in the table?

4 calories per minute

15 calories per minute

40 calories per minute

60 calories per minute

Multiple Choice

Find the rate of change in the table.

-3

Not a constant rate/Non-Linear

Equations

If we remember from 7th grade,
$k=\frac{y}{x}$ . y is the dependent variable. x is the independent variable.
To write the unit rate (k) in an equation, it is usually in the form $y=kx$ . In 8th grade, it is y=kx+n.
Unit rate is the same as the rate of change

Equations continued. . .

Simply put, to identify the rate of change in an equation, we need to look for the form y=kx + n and choose the number next to the independent variable.

Example

If you were given the equation, y=2x, my rate of change is 2.
If you were given the equation, h=46s, my rate of change is 46.
If you were given d=101t, my rate of change is 101.
If you were given w=11x-2, my rate of change is 11.
If you were given z=3+19x, my rate of change is 19.
If you were given y=mx+b, my rate of change is m.

Multiple Choice

In the equation y = 14x, what is the constant of proportionality?

Multiple Choice

What is the rate of change in the following equation: y = - 4x - 5 ?

- 4

- 4x

- 5

Multiple Choice

In the equation y = 7-14x, what is the rate of change?

-14

Multiple Choice

What is the rate of change in the equation: d= 1/2t +3

1/2

-3

Multiple Choice

Identify the rate of change:

h=-9-3s

-9

-3

Multiple Choice

What is the rate of change in the equation: y=2x-4?

-4

-2

Verbal Problems

Verbal problems are the same as word problems. In word problems, the rate of change is the "thing" that is always changing.

Example

Multiple Choice

A man is climbing down from 100 feet high descending 30 feet per minute. What is the rate of change?

-30

100

-100

Multiple Choice

Mr. Z is starting his own car club, there is a $30 join up fee and a $5 monthly fee. What is the rate of change?

Multiple Choice

What is the rate of change?

9.25

1.25

19.25

0.25

Multiple Choice

Mr. Blackman was administering a test. He heard one of the scholars talking and decided to take 5 points away from everyone's test score. What is the rate of change?

There is none.

100

-5

Self Reflection

Poll

Today I felt like I mastered how to . . .

Accurately identify the rate of change in a table

Accurately identify the rate of change in a equation

Accurately identify the rate of change in a verbal problem

Rate of Change

I can identify the rate of change.

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