Bell Work

1. Get your tracking folder.2. Read through the current scale (LG # 808).3. Check off any boxes we have learned about and

you have mastered.4. Rate yourself at your current level.5. Write about why you rated yourself that level,

using specific evidence from the scale (on the same side as the level 2).

13-2B Represent

Linear Functions

Represent Linear Functions

Vocabulary

• Functions can be represented in words, in a table, as an equation, with a graph, and as ordered pairs.

• The x-intercept is where the graph crosses the x-axis

• The y-intercept is where the graph crosses the y-axis

Graph a Function

Graph a Function

Real-World Example

Check Your Progress

a) The school bookstore sells spiral notebooks x for $3 and pocket folders y for $1. Graph the function 3x + y = 10 to find the number of each that can be bought with $10.

How to Represent Functions

Discrete or Continuous?

Discrete and Continuous

Discrete and Continuous

Check Your Progress

Kareem is mowing lawns to earn money. He deposits $50 into his savings account every Friday. He already had $200.

b) How much money will Kareem have after 24 weeks?

c) Is this situation continuous or discrete?

5-2AB Constant Rate of Change

Rate of ChangePet Care: The prices of the Happy House Pet

Care are listed in the table. Use the graph to determine how the number of hours is related to the cost.

1. Is the graph linear?2. What is the cost per hour (unit rate) charged by the Happy

Hound?3. Look at the ordered pairs for hours 2 and 3. How do the values

change? 4. Is the relationship the same for all consecutive values in the

table?5. Use the graph to examine any two consecutive points. By how

much does y change? By how much does x change?6. How does this change relate to the unit rate?

Vocabulary

• Linear• Rate of Change• Constant Rate of Change

How to Find Rate of Change from Table

1) Choose 2 points2) Represent it as Change in Output (dependent-y) Change in Input (independent-x)3) Put it in terms of unit rate

80-40 = $40 = $8 10-5 5 cars 1 car

If the rate of change is constant the relationship is linear, we will call this rate the

SLOPE when write equations.

You Try

Find the Rate of Change from the table.

Is it a constant rate of change?

How to find Rate of Change from a Graph

1) Make a stair between 2 points2) Represent the change as:

Change in vertical axis (y)Change in horizontal axis(x)

**Also known as rise/run3) Write as unit rate

Example of Rate of Change from a Graph

You Try• Find the constant rate of change from the

graph

Rate yourself using the bookmark!

RiseRun

Slope

Vocabulary

• Notice: THIS IS THE SAME AS CONSTANT RATE OF CHANGE

Slope Formula

Given 2 points:Point 1 (x1, y1) and Point 2 (x2,y2)

y2 -y1

x2 -x1

Example: Find the Slope

b) What is the slope of the line that goes through the points (5,3) and (-1, 4)?

Slope!Positive Slope Negative Slope

Zero Slope No Slope or Undefined

Slope Video

• http://www.youtube.com/watch?v=FmIhlc1bJuA

You Try

• The table below shows the number of small packs of fruit snacks y per box x.

a) Graph the data. b) Find the slope of the line.c) Explain what the slope means.d) Is your slope positive, negative, zero, or

undefined?

You Try

• At 2:00 pm, the temperature is 81 degrees F. At 3:00 pm the temperature is 78 degrees F. Create a table of temperature versus time if temperature continues to decrease at this rate from 2:00 to 6:00 pm. Find the value of the slope and interpret it in words.

How to find Slope from a Graph

1) Identify 2 points.2) Use the slope formula.

3) Check that it makes sense: (Is the slope positive when the graph shows a positive slope?)

Finding Slope from a Graph

You Try

Exit Pass

• Describe the relationship between the rate of change and the slope. How do you find each?