Rate of Change

Rate of Change

I can 
● Determine slope from a graph
● Determine slope from a table
● Determine slope from ordered pairs

Open Ended

Determine the ordered pairs of the points that are labeled on the graph.

Rate of Change Lesson

During this lesson, there will be slides that will give you definitions and examples. You should be taking notes during these slide. There will also be slides where you will be asked to answer questions. Please answer the questions to your best ability. 

What is rate of change?

• A constant rate of change is when the rate of change between any two quantities remains the same. This is a linear relationship. 

• The slope is a constant rate of change for a linear relationship. 

Multiple Choice

Which of these graphs has a negative slope?

Multiple Choice

Which of these graphs has an undefined slope?

Multiple Choice

Which of these graphs has no slope?

Multiple Choice

Which of these graphs has a positive slope?

Slope of a graph can be represented by the fraction:

rise/run

Let's find the slope of this graph.

1. Find two point on the function (it can be any two points!)

Let's find the slope of this graph.

2. From the point on the left draw a vertical line and a horizontal line to connect the two points. (It will look like a triangle!)

Let's find the slope of this graph.

3. Find the height of your vertical line. Make sure you are using positive (up) and negative (down) for your direction. (rise)

Let's find the slope of this graph.

3. Find the length of your horizontal line. Make sure you are using positive (right) and negative (left) for your direction. (run)

Let's find the slope of this graph.

3. Find the rise over run. 

Rise = 5, run =2.

rise/run = 5/2
Answer = 5/2

Multiple Choice

Find the slope.

• -2

• 
  

  $\frac{1}{2}$

• 2

• $-\frac{1}{2}$
  

Multiple Choice

Find the slope.

• -2

• $\frac{1}{2}$

• 2

• $-\frac{1}{2}$

To find the rate of change of a table, determine the pattern of the y values and x values

(change in y)/(change in x)

Let's find the slope from a table. 

1. Find the change in x. (What do you add or subtract by to get the next value?)

Let's find the slope from a table. 

2. Find the change in y. (What do you add or subtract by to get the next value?)

Let's find the slope from a table. 

3. Find the (change in y)/(change in x). 

change in y = 10
change in x =2
(change in y)/(change in x) = 10/2
Answer: 5

Let's find the slope from a table. 

1. Find the change in x. (What do you add or subtract by to get the next value?)

Let's find the slope from a table. 

2. Find the change in y. (What do you add or subtract by to get the next value?)

Let's find the slope from a table. 

3. Find the (change in y)/(change in x). 

change in y = -1
change in x = 6
(change in y)/(change in x) = 6/-1
Answer: -6

Multiple Choice

Find the slope.

• $\frac{2}{3}$

• $-\frac{2}{3}$

• $\frac{3}{2}$

• $-\frac{3}{2}$

Multiple Choice

Find the slope.

•  $\frac{3}{4}$  

•  $-\frac{3}{4}$ 

•  $\frac{4}{3}$ 

•  $-\frac{4}{3}$  

To find the slope between two points, use the formula:

(y2 - y1)/(x2 - x1) when (x1, y1) and (x2, y2)

To find the slope between two points, use the formula:

1. Identify (x1, y1) and (x2, y2).

To find the slope between two points, use the formula:

2. Put the values into the slope formula.

To find the slope between two points, use the formula:

3. Simplify the formula.

Answer: 1/2

To find the slope between two points, use the formula:

1. Identify (x1, y1) and (x2, y2).

To find the slope between two points, use the formula:

2. Put the values into the slope formula.

To find the slope between two points, use the formula:

3. Simplify the formula.

Answer: 1/3

Multiple Choice

Find the slope between

 $\left(3,\ 0\right)\ and\ \left(-11,\ -15\right)$  

•  $\frac{14}{15}$  

•  $-\frac{14}{15}$  

•  $\frac{15}{14}$  

•  $-\frac{15}{14}$  

Multiple Choice

Find the slope between

 $\left(-4,\ 7\right)\ and\ \left(-6,\ -4\right)$  

•  $\frac{11}{2}$  

•  $-\frac{11}{2}$  

•  $\frac{2}{11}$  

•  $-\frac{2}{11}$  

Checkpoint

Answer the following questions to check your understanding of this lesson.

Multiple Choice

Which of these graphs has no slope?

Multiple Choice

Find the slope.

• -2

• 
  

  $\frac{1}{2}$

• 2

• $-\frac{1}{2}$
  

Multiple Choice

Find the slope.

•  $\frac{3}{4}$  

•  $-\frac{3}{4}$ 

•  $\frac{4}{3}$ 

•  $-\frac{4}{3}$  

Multiple Choice

Find the slope between

 $\left(3,\ 0\right)\ and\ \left(-11,\ -15\right)$  

•  $\frac{14}{15}$  

•  $-\frac{14}{15}$  

•  $\frac{15}{14}$  

•  $-\frac{15}{14}$  

Multiple Select

Evaluate your ability and understanding of determining the constant rate of change of linear functions:

• No Understanding

• Still need some help

• Good to go

• Have mastered it

• Could teach the lesson