Unit 4 Lesson 1 FINAl

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When do you want to retire?

 _{If you work till the traditional retirement age of 65, you should have 12}

times your annual household income saved.

 _{For someone earning $100,000 a year, that’s $1.2 million.}

 _{But if you want to quit work at age 55 and replace 75% of your income,}

you’ll need 18 times your annual income or $1.8 million.

 _{If you start saving now, you can save 10% to 15% of your annual}

income starting at 22 …

 _{let’s say you make $40K when you graduate, you need to save $4K of that}

each year (~$300/month)

Your money’s

rate of change is

a real life

application of

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Slope in the Real World

 _{Slope is a measure of steepness. Some}

real life examples of slope include:

 _{in building roads one must figure out how steep} the road will be

 _{skiers/snowboarders need to consider the slopes} of hills in order to judge the dangers, speeds, etc

 _{when constructing wheelchair ramps, slope is a} major consideration

 _{when building stairs, one must consider the} slope of them so they are not too steep to walk on

Can you think

of anymore

examples of

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Objectives

 _{Identify a linear parent function.}

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What equations belong in the family?

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Example 1A: Identifying a Linear Function by Its Graph

Identify whether the graph represents a function. Explain. If the graph does represent a function, is the function linear?

Each domain value is paired with exactly one range value. The graph forms a line.

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Example 1B: Identifying a Linear Function by Its Graph

Each domain value is paired with exactly one range value. The graph is not a line.

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Example 1C: Identifying a Linear Function by Its Graph

The only domain value,

–2, is paired with many different range values.

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Check It Out! Example 1a

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Check It Out! Example 1b

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Check It Out! Example 1c

Each domain value is not paired with exactly one range value.

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Example 1: Finding Slope by Using the Slope Formula

Find the slope of the line that contains (2, 5) and (8, 1).

Use the slope formula.

Substitute (2, 5) for (x

₁

, y

₁

) and

(8, 1) for (x

₂

, y

₂

).

Simplify.

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Find the slope of the line that contains (–2, –2) and (7, –2).

Substitute (–2,

–

2) for (x

₁

, y

₁

) and

(7, –2) for (x

₂

, y

₂

).

Simplify.

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Find the slope of the line that contains (5, –7) and (6, –4).

Substitute (5, –7) for (x

₁

, y

₁

) and

(6, –4) for (x

₂

, y

₂

).

Simplify.

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Find the slope of the line that contains and Check It Out! Example 1c

Substitute for (x

₁

, y

₁

)

and for (x

₂

, y

₂

) and

simplify.

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Sometimes you are not given two points

to use in the formula. You might have to

choose two points from a graph or a

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Example 2A: Finding Slope from Graphs and Tables

The graph shows a linear relationship. Find the slope.

Let (0, 2) be (x₁, y₁) and (–2, –2) be (x₂, y₂).

Simplify.

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Example 2B: Finding Slope from Graphs and Tables

The table shows a linear relationship. Find the slope.

Step 1 Choose any two points from the table. Let (0, 1) be (x₁, y₁) and (–2, 5) be (x₂, y₂).

Step 2 Use the slope formula.

The slope equals −2

Substitute (0, 1) for

and (–2, 5) for _.

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The graph shows a linear relationship. Find the slope.

Simplify.

Use the slope formula.

Let (2, 2) be (x₁, y₁) and (4, 3) be (x₂, y₂).

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Simplify.

Use the slope formula.

Let (–2, 4) be (x₁, y₁) and (0, –2) be (x₂, y₂).

Substitute (–2, 4) for (x

₁

, y

₁

)

and (0, –2) for (x

₂

, y

₂

).

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Check It Out! Example 2c

Step 1 Choose any two points from the table. Let (0, 1) be (x₁, y₁) and (2, 5) be (x₂, y₂).

Use the slope formula.

Simplify.

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Check It Out! Example 2d

Step 1 Choose any two points from the table. Let (0, 0) be (x₁, y₁) and (–2, 3) be (x₂, y₂).

Use the slope formula.

Simplify

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Remember that slope is a rate of change.

In real-world problems, finding the slope

can give you information about how a

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Example 3: Application

The graph shows the average electricity

costs (in dollars) for operating a

refrigerator for several months. Find the slope of the line. Then tell what the slope represents.

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Example 3 Continued

Step 2 Tell what the slope represents.

In this situation y represents the cost of electricity and x represents

time.

So slope represents in units of .

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Check It Out! Example 3 The graph shows the height of a plant

over a period of days. Find the slope of the line. Then tell what the slope represents.

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Check It Out! Example 3

Step 2 Tell what the slope represents.

In this situation y represents the height of the plant and x represents

time.

So slope represents in units of .

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If you know the equation that describes

a line, you can find its slope by using any

two ordered-pair solutions. It is often

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Example 4: Finding Slope from an Equation

Find the slope of the line described by 4x – 2y = 16.

Step 1 Find the x-intercept. Step 2 Find the y-intercept.

4x – 2y = 16

4x = 16

x = 4

Step 3 The line contains (4, 0) and (0, –8). Use the slope formula. 4x – 2y = 16

–2y = 16

y = –8

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Check It Out! Example 4

Find the slope of the line described by 2x + 3y = 12.

Step 1 Find the x-intercept. Step 2 Find the y-intercept.

2x + 3y = 12 2x + 3y = 12

2x + 3(0) = 12 Let y = 0. 2(0) + 3y = 12 _{Let x = 0.} 2x = 12

x = 6

3y = 12

y = 4

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