SLOPE WORD PROBLEMS

SLOPE WORD PROBLEMS Lesson Objective: 4.01a

Students will know how to solve word problems using slope

SLOPE 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?

SLOPE 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!

SLOPE WORD PROBLEMS Remember the slope equation:

In order to find the slope we need two points

m = y2 – y1x2 – x1

SLOPE 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 x2 with the second year and x1 with the first

y2 – y1m = x2 – x12010 – 2005

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

y2 – y1m = 2010 – 200513 – 3

SLOPE 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 – 200513 – 3 10

52

SLOPE 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?

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

m = 2

SLOPE 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?

SLOPE 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.

SLOPE 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

(x1, y1), (x2, y2)(1995, y1), (1999, y2)(1995, 16000), (1999, 19000)

SLOPE WORD PROBLEMS

Replace y2 with 19000 and y1 with 16000

Replace x2 with 1999 and x1 with 1995 Simplify the top and the bottom Reduce the fraction

(1995, 16000), (1999, 19000)m =y2 – y1

x2 – x119000 – 16000 1999 – 1995 3000

4750

SLOPE 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?

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

m = 750

SLOPE WORD PROBLEMS 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?

SLOPE 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?

SLOPE 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?