lesson objective: 4.01a students will know how to solve word problems using slope
TRANSCRIPT
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 – y1
x2 – 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 – x1
19000 – 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?