THE ULTIMATE
Slope/Y-intercept
Handbook
By Mary Foster
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Arkanasas State StandardLoading...
HSS.ID.C.7: Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the dataCar Wash
Lets say you and a friend are going to start a car wash to make money. You have to buy some supplies first, totaling about $100. Then, you want to charge $5 per car wash. Lets make a chart showing how much money P, you would profit from washing x cars.
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Why do you think that the profit is negative before you start washing cars?
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So what is the slope and what does it mean?
So what IS the rate of change??
In this table, I have highlighted the things that are changing in yellow and the things that are not changing in RED.
The SLOPE is defined as the RATE OF CHANGE
So what IS the rate of change??
In this case, the yellow numbers are what will change. After one car wash, it is going up by 5, after two car washes, it is going up by 10, etc.
Each time you increase the x by one the profit goes up by ______ ?
The SLOPE is defined as the RATE OF CHANGE
You guessed it! 5!!! So the slope is 5. For every additional car wash, the profit will increase by $5.
What about the y-Intercept?
What is NEVER changing in the calculations we did?
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It's the RED number, -100