document.write( "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. \n" ); document.write( "
Algebra.Com's Answer #492203 by mathgranny(13)\"\" \"About 
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Some students have trouble understanding what the variables x and y represent.\r
\n" ); document.write( "\n" ); document.write( " I like to use letters that remind us of what the variables represent.
\n" ); document.write( " I would use C to represent total Cost and n to represent #of miles traveled.\r
\n" ); document.write( "\n" ); document.write( "I call the 2 variables the Output variable and the Input variable.\r
\n" ); document.write( "\n" ); document.write( " First I find the rate of change in the paragraph.
\n" ); document.write( " I write the rate of change as number Word per Word.
\n" ); document.write( " In this problem: .25 dollars per mile.
\n" ); document.write( " The word right after the number represents the Output variable
\n" ); document.write( " and is placed on the vertical axis. Some students might use D for dollars
\n" ); document.write( " but after doing enough of these problems I convince them that since
\n" ); document.write( " dollars is used to represent your cost, we should use C.
\n" ); document.write( " The word after the word \"per\" represents the input variable , number of miles.
\n" ); document.write( " Where does the equation come from.?
\n" ); document.write( " Think about paying. For your cab ride.
\n" ); document.write( "Describe in word how to find your total Cost.
\n" ); document.write( " Total cost = my initial 12 dollars plus 25 cents for each mile traveled.
\n" ); document.write( " We usually put the initial cost at the end .
\n" ); document.write( " Total cost = 25 cents for each mile plus the initial 12 dollars.
\n" ); document.write( " Translate from verbal to algebraic .
\n" ); document.write( " C = .25 n + 12
\n" ); document.write( " Then the variable C is placed on the vertical axis, and \"n\" along the vertical.
\n" ); document.write( " Usually we use y for the input and x for the input.
\n" ); document.write( " y = .25x + 12
\n" ); document.write( " We make a table and graph the equation.
\n" ); document.write( " We can know ahead of time that we will get a straight line because any equation
\n" ); document.write( " written in this form gives us a straight line.
\n" ); document.write( " Graphing , we see that the point there the line crosses the vertical axis is ( 0, 12)
\n" ); document.write( " Remember all points are written as (x,y) Or (input, output)
\n" ); document.write( " Many students cannot tell us the MEANING of the y intercept.
\n" ); document.write( " Write the intercept as the point (0,12), but in include the input and output units.
\n" ); document.write( " We have (0 miles, 12 dollars) meaning, when we have traveled 0 miles, the cost
\n" ); document.write( " is 12 dollars. Or 12 dollars is the starting cost.
\n" ); document.write( " Look at your graph and find the slope, using units.
\n" ); document.write( " The slope is .25 (dollars per mile). THE SLOPE is the number in front
\n" ); document.write( " of the input variable in our equation.\r
\n" ); document.write( "\n" ); document.write( " So for any linear equation. we have
\n" ); document.write( " Y = mx + b
\n" ); document.write( " meaning.
\n" ); document.write( "Output variable. = slope (input variable) + value of y-intercept. \n" ); document.write( "
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