Date post: | 31-Dec-2015 |
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Slippery SlopesA lesson on interpreting slope and y-intercept
in real world examples
Standard:MAFS.912.S-ID.3.7:
Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.
Problem of the Day:
Solve for the slope between (-1,-5) and (6,9).
m=2
m= y2-y1 x2-x1
m= 9-(-1) 6-(-1)
m= 14 7
VocabularySlope intercept form- y=mx+b, where m is slope and b is the y-intercept
Slope- Change in y over change in x (rate of change)
Y-intercept- the value of y when x is zero
Example of Slope in a Real World Scenario
m= Change in height Change in time
The graph to the right shows the growth of a tree at a constant rate, over a period of four years. Interpret the slope of the line.
Example of Slope in a Real World Scenario
m= change in distance change in time
Click icon to add picture
Example of Y-Intercept in a Real World Scenario.
For example: The y-intercept in this graph is 1080, meaning it is the amount the person owes before he/she began making payments. (zero payments have been made, $1080 owed)
The graph then shows that over the next 24 months this debt will be paid off.
Example of Y-Intercept in a Real World Scenario
You have 300 items of clothing and decide to start donating to Goodwill. Your y-intercept is the amount of clothing you have before you start donating to Goodwill every month.
Solving a Real World ExampleA student is eating an
ice cream cone at the park that is 12.7cm tall. It is extremely hot outside and the ice cream starts to melt at a constant rate of 2cm/minute. If the student didn’t eat any of the ice cream and it started to melt, how much would be left after 3 minutes?
1st: Identify the slope and y-intercept
2nd: Plug into slope intercept formY=-2x+12.7 (slope is
negative because it is decreasing in size)
3rd: Plug in 3 for x since we want to know how tall it will be after 3 minutes
4th: Solvey=-2(3)+12.7y=-6+12.7y=6.7
Understand that after 3 minutes of melting the ice cream cone will now measure 6.7cm.
Leaky Lines ProjectItems you should
have:400ml of water500ml+ graduated
cylinderEmpty water bottleStopwatch
Leaky Lines ProjectGet into groups of
twoOne person will hold
the water bottle and be in charge of the stopwatch
Measure 400ml into bottle
Turn water bottle over and start timer
Every 10 seconds record how much water has accumulated in the cylinder
Leaky Lines ProjectCreate a graph based
on the data gathered graphing the time intervals on the x-axis and the amount of milliliters on the y-axis.
Solve for the rate of change between two coordinates.
Write the equation of the line.
Discussion:Is the slope positive
or negative?What is the y-
intercept?
Independent PracticeHad we been
measuring the rate at which the water left the bottle, would the slope have been positive or negative?
What would the y-intercept have been?
Write an equation expressing this linear relationship using m for slope.
Review for Quiz1. Your family is taking a trip to Disney and is
driving at a constant rate. After one hour, you have traveled 60 miles, and after 2 hours you have traveled 120 miles. How fast is the car going?
2. You are selling candy bars for a fundraiser. You have raised $50 so far and sell each candy bar for 75 cents. How much money will you have made after selling 30 candy bars?
Review for Quiz ContinuedThe graph shows the
amount of money you have at the beginning of the month.
a. How much money did you begin with? b. How much money do you earn each week? c. How much money will you have after 3 weeks?