algebra 2 bellwork 9/15/2014 atlanta, ga has an elevation of 15 ft above sea level. a hot air...

Algebra 2Algebra 2

Bellwork 9/15/2014Bellwork 9/15/2014

Atlanta, GA has an elevation of 15 ft above sea level. A hot air balloon taking off from Atlanta rises 40 ft/min. Write an equation to model the balloon's elevation as a function of time. Interpret the intercept of which the graph intersects the vertical axes.

Algebra 2Algebra 2

Using Linear ModelsUsing Linear Models

Lesson 2-4

Suppose an airplane descends at a rate of 300 ft/min from

an elevation of 8000 ft.

Write and graph an equation to model the plane’s elevation as a function of the time it has been descending. Interpret the intercept at which the graph intersects the vertical axis.

Relate: plane’s elevation = rate • time + starting elevation .

Define: Let t = time (in minutes) since the plane began its descent.

Let d = the plane’s elevation.

Write: d = –300 • t + 8000

Additional Examples

Algebra 2Algebra 2

Using Linear ModelsUsing Linear Models

Lesson 2-4

(continued)

An equation that models the plane’s elevation is d = –300t + 8000.

The d-intercept is (0, 8000).

This tells you that the elevation of the plane was 8000 ft at the moment it began its descent.

Additional Examples

Algebra 2Algebra 2

Using Linear ModelsUsing Linear Models

Lesson 2-4

A spring has a length of 8 cm when a 20-g mass is hanging

at the bottom end. Each additional gram stretches the spring

another 0.15 cm. Write an equation for the length y of the spring as

a function of the mass x of the attached weight. Graph the equation.

Interpret the y-intercept.

Step 1: Identify the slope.

0.15 or 3/20

Additional Examples

Algebra 2Algebra 2

Using Linear ModelsUsing Linear Models

Lesson 2-4

(continued)

Step 2:

Additional Examples

Use one of the points and the slope-intercept form to write an equation for the line.

y = mx + b Use the slope-intercept form.

8 = 3/20(20) + b Substitute.

8 = 3 + b

5 = b   

y = 0.15x + 5 Solve for y.

Algebra 2Algebra 2

Using Linear ModelsUsing Linear Models

Lesson 2-4

(continued)

An equation of the line that models the length of the spring is y = 0.15x + 5.

The y-intercept is (0, 5). So, when no weight is attached to the spring, the length of the spring is 5 cm.

Additional Examples

Algebra 2Algebra 2

Using Linear ModelsUsing Linear Models

Lesson 2-4

Use the equation from Additional Example 2. What mass

would be needed to stretch the spring to a length of 9.5 cm?

y = 0.15x + 5 Write the equation.

9.5 = 0.15x + 5 Substitute 9.5 for y.

30 = x Simplify.

The mass should be 30 g.

= x Solve for x.9.5 – 5

0.15

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Algebra 2Algebra 2

Using Linear ModelsUsing Linear Models

Scatter Plot: graph that relates two different sets of data by plotting the data as ordered pairs.

Algebra 2Algebra 2

Using Linear ModelsUsing Linear Models

A B C

DE

No CorrelationWeak Positive CorrelationWeak Negative CorrelationStrong Positive CorrelationStrong Negative Correlation

Algebra 2Algebra 2Lesson 2-4

An art expert visited a gallery and jotted down her guesses

for the selling price of five different paintings. Then, she checked the

actual prices. The data points (guess, actual) show the results, where

each number is in thousands of dollars. Graph the data points.

Decide whether a linear model is reasonable. If so, draw a trend line

and write its equation.

{(12, 11), (7, 8.5), (10, 12), (5, 3.8), (9, 10)}

A linear model seems reasonable since the points fall close to a line.

Trend lines and equations may vary.

Using Linear ModelsUsing Linear Models

Additional Examples

Algebra 2Algebra 2

Using Linear ModelsUsing Linear Models

Lesson 2-4

(continued)

A linear model seems reasonable since the points fall close to a line. A possible trend line is the line through (6, 6) and (10.5, 11). Using these two points to write an equation in slope-intercept form gives

y = x – .109

23

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Algebra 2Algebra 2

Using Linear ModelsUsing Linear Models