Lesson 9

Unit 5 - Lesson 9: Linear Models

A candle is burning. It starts out 12 inches long. After 1 hour, it is 10 inches long. After 3 hours, it is 5.5 inches long.

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9.1 Candlelight

Poll

When do you think the candle will burn out completely?

• 4 hours

• 5 hours

• 6 hours

• 7 hours

Poll

Is the height of the candle a function of time?

• yes

• no

A LINEAR MODEL will result in a linear equation of the form y = mx + b and create a straight line.

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Linear Models

Poll

If you answered Yes to the previous question, is it a LINEAR FUNCTION. Meaning does the height of the candle decrease at the same rate every hour?

• Yes

• No

Multiple Choice

A 7-inch candle burns at a rate of 2-inches per hour. Which equation represents the relationship between y, the height of the candle in inches, and x, the number of hours the candle burns?

• y = 2x + 7

• y = 7 - 2x

• y = 2 - 7x

• y = 7x + 2

Multiple Choice

* The amount of water in gallons, A, in Tank A is given by the function A = 200 + 8t, where t is minutes.

* The amount of water in gallons, B, in Tank B starts at 400 gallons and is decreasing at 5 gallons per minute. These functions work when t $$\ge$$ 0 and t $$\le$$ 80.

- Which tank started out with more water?

• Tank A

• Tank B

Multiple Select

* The amount of water in gallons, A, in Tank A is given by the funciton A = 200 + 8t, where t is minutes.

* The amount of water in gallons, B, in Tank B starts at 400 gallons and is decreasing at 5 gallons per minute. These functions work when t $$\ge$$ 0 and t $$\le$$ 80.

- One tank is filling up. The other is draining out. Which is which? Select all that apply.

• Tank if is draining out

• Tank B is draining out

• Tank B is filling up

• Tank A is filling up

Multiple Choice

On the first day after the new moon, 2% of the Moon's surface is illuminated. On the second day, 6% is illuminated.

*Based on this information, predict the day on which the Moon's surface is 50% illuminated.

• day 11

• day 12

• day 13

• day 14

Multiple Choice

On the first day after the new moon, 2% of the Moon's surface is illuminated. On the second day, 6% is illuminated.

*Based on this information, predict the day on which the Moon's surface is 100% illuminated.

• day 24

• day 25

• day 26

• day 27

Multiple Choice

The Moon's surface is 100% illuminated on day 14. Does this agree with the prediction you made?

• yes

• no

Multiple Choice

Is the percentage illumination of the Moon's surface a linear funciton of the day?

• yes

• no

Multiple Choice

In science class, Jada uses a graduated cylinder with water in it to measure the volume of some marbles. After dropping in 4 marbles so they are all under water, the water in the cylinder is at a height of 10 milliliters. After dropping in 6 marbles so they are all under water, the water in the cylinder is at a height of 11 milliliters.

- What is the volume of 1 marble?

• 0.5ml

• 1ml

• 1.5ml

• 0ml