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Slope Word Problems

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Slope Word Problems

Lesson Objective: 4.01a

Students will know how to solve word problems using slope

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?

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!

Remember the slope equation:

In order to find the slope we need two points

y2 – y1

m =

x2 – x1

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 x2 with the second year and x1 with the first

y2 – y1

m =

x2 – x1

2010 – 2005

Replace y2 with the height from the second year and y1 with the first

y2 – y1

13 – 3

m =

2010 – 2005

Simplify the top

Simplify the bottom

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

10

13 – 3

m =

2

2010 – 2005

5

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

m = 2

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?

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.

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

(1995, 16000), (1999, 19000)

(1995, y1), (1999, y2)

(x1, y1), (x2, y2)

Replace y2 with 19000 and y1 with 16000

Replace x2with 1999 and x1with 1995

Simplify the top and the bottom

Reduce the fraction

(1995, 16000), (1999, 19000)

y2 – y1

19000 – 16000

3000

m =

750

x2– x1

1999 – 1995

4

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

m = 750

Monica feeds her dog the same amount of dog food each day from a very large bag. ON the 3rd day, she has 44 cups left in the bag, and on the 11th day she has 28 cups left. How many cups of food does she feed her dog a day?

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?

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?