Question 817783: A cab company charges $12 for each trip plus $.25 per mile. Write the equation (y=mx+b). Identify the slope and y-intercept. Write a sentence identifying the x and y variables. Label and graph.
Found 2 solutions by stanbon, mathgranny:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A cab company charges $12 for each trip plus $.25 per mile. Write the equation (y=mx+b). Identify the slope and y-intercept. Write a sentence identifying the x and y variables. Label and graph.
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y = 0.25x + 12
slope = 0.25
y-int = 12
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x is # of miles
y is total cost
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Cheers,
Stan H.
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Answer by mathgranny(13) (Show Source):
You can put this solution on YOUR website! Some students have trouble understanding what the variables x and y represent.
I like to use letters that remind us of what the variables represent.
I would use C to represent total Cost and n to represent #of miles traveled.
I call the 2 variables the Output variable and the Input variable.
First I find the rate of change in the paragraph.
I write the rate of change as number Word per Word.
In this problem: .25 dollars per mile.
The word right after the number represents the Output variable
and is placed on the vertical axis. Some students might use D for dollars
but after doing enough of these problems I convince them that since
dollars is used to represent your cost, we should use C.
The word after the word "per" represents the input variable , number of miles.
Where does the equation come from.?
Think about paying. For your cab ride.
Describe in word how to find your total Cost.
Total cost = my initial 12 dollars plus 25 cents for each mile traveled.
We usually put the initial cost at the end .
Total cost = 25 cents for each mile plus the initial 12 dollars.
Translate from verbal to algebraic .
C = .25 n + 12
Then the variable C is placed on the vertical axis, and "n" along the vertical.
Usually we use y for the input and x for the input.
y = .25x + 12
We make a table and graph the equation.
We can know ahead of time that we will get a straight line because any equation
written in this form gives us a straight line.
Graphing , we see that the point there the line crosses the vertical axis is ( 0, 12)
Remember all points are written as (x,y) Or (input, output)
Many students cannot tell us the MEANING of the y intercept.
Write the intercept as the point (0,12), but in include the input and output units.
We have (0 miles, 12 dollars) meaning, when we have traveled 0 miles, the cost
is 12 dollars. Or 12 dollars is the starting cost.
Look at your graph and find the slope, using units.
The slope is .25 (dollars per mile). THE SLOPE is the number in front
of the input variable in our equation.
So for any linear equation. we have
Y = mx + b
meaning.
Output variable. = slope (input variable) + value of y-intercept.
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