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Slope Word Problems

Slide2Slope Word Problems

Lesson Objective: 4.01a

Students will know how to solve word problems using slope

Slide3Slope Word Problems

In 2005, Joe planted a tree that was 3 feet tall. In 2010, the tree was 13 feet tall. Assuming the growth of the tree is linear

,

what was the rate of growth of the tree?

Slide4Slope Word Problems

In 2005, Joe planted a tree that was 3 feet tall. In 2010, the tree was 13 feet tall. Assuming the growth of the tree is linear, what was the rate of growth of the tree?

What does “rate of growth” mean?

Slope!

Slide5Slope Word Problems

Remember the slope equation:

In order to find the slope we need two points

m =

y

2

– y

1

x

2

– x

1

Slide6Slope Word Problems

In 2005, Joe planted a tree that was 3 feet tall. In 2010, the tree was 13 feet tall. Assuming the growth of the tree is linear, what was the rate of growth of the tree?

Remember, x is always years, so replace x

2

with the second year and x

1

with the first

y

2

– y

1

m =

x

2 – x1

2010 – 2005

Slide7Slope Word Problems

In 2005, Joe planted a tree that was 3 feet tall. In 2010, the tree was 13 feet tall. Assuming the growth of the tree is linear, what was the rate of growth of the tree?

Replace

y

2

with the height from the second year and y

1

with the first

y

2

– y

1

m =

2010 – 200513 – 3

Slide8Slope Word Problems

Simplify the top

Simplify the bottom

Simplify the fraction to get m. Keep it as a fraction if it can’t be simplified

m =

2010 – 2005

13 – 3

10

5

2

Slide9Slope Word Problems

The slope is 2, so the tree grows 2 feet per year

m = 2

Slide10Slope Word Problems

In 1995 a public library had 16,000 books on its shelves. In 1999 the library had 19,000 books. Assuming a linear increase, how many books were added to the library each year?

Slide11Slope Word Problems

In 1995 a public library had 16,000 books on its shelves. In 1999 the library had 19,000 books. Assuming a linear increase, how many books were added to the library each year?

We’re looking for how many for each year, usually the word “each” means slope.

Slide12Slope Word Problems

In 1995 a public library had 16,000 books on its shelves. In 1999 the library had 19,000 books. Assuming a linear increase, how many books were added to the library each year?

Years are always x so replace the

x’s

with the years

Replace the

y’s

with the number of books for each year

(x

1

, y

1

), (x2

, y2)(1995,

y

1

),

(1999,

y

2

)

(1995, 16000), (1999, 19000)

Slide13Slope Word Problems

Replace y

2

with 19000 and y

1

with 16000

Replace

x

2

with

1999 and x1 with 1995Simplify the top and the bottomReduce the fraction

(1995, 16000), (1999, 19000)m =y

2 – y1x

2

–

x

1

19000 – 16000

1999 – 1995

3000

4

750

Slide14Slope Word Problems

m = 750, therefore the library adds 750 books each year

m = 750

Slide15Slope Word Problems

Monica feeds

her

dog the same amount of dog food each day from a very large bag. ON the 3

rd

day, she has 44 cups left in the bag, and on the 11

th

day she has 28 cups left. How many cups of food does she feed her dog a day?

Slide16Slope Word Problems

Wendy bought a car for $25,000 and its value depreciated linearly. After 3 years the value was $21,250. What was the amount of yearly depreciation?

Slide17Slope Word Problems

Jamal’s parents give him $20 to spend at camp. Jamal spends the same amount of money on snacks each day. After 4 days he has $12 left. How much money is he spending

each day?

Slide18Slide19

## Slope Word Problems Slope Word Problems

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