SOLUTION: Phil Taylor works as a service station attendant. He earns a weekly salary of $280 plus $10.50 per hour for overtime over 40 hours.
1) Write an equation that you can use to find
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-> SOLUTION: Phil Taylor works as a service station attendant. He earns a weekly salary of $280 plus $10.50 per hour for overtime over 40 hours.
1) Write an equation that you can use to find
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Question 159799: Phil Taylor works as a service station attendant. He earns a weekly salary of $280 plus $10.50 per hour for overtime over 40 hours.
1) Write an equation that you can use to find Phil’s weekly earnings.
2) What do you think is a reasonable domain for the function.
3) Find the range for the domain in #2.
4) Graph the equation.
5) What is the vertical intercept of the graph? Explain the meaning of the vertical intercept in terms of the situation.
6) What is the slope of the graph? Explain the meaning of the slope in terms of the situation.
You can put this solution on YOUR website! Salary is $280 per week for a 40 hour week plus $10.95 * (hours worked over 40)
let x = hours worked over 40
let S = Salary
then S = 280 + 10.95 * x
removing the parentheses, the equation becomes S = 280 + 10.95 * x
this becomes S = 10.95 * x + 280
to graph this equation, let y = S
equation becomes y = 10.95 * x + 280
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a graph of this equation looks like this.
please scan below the graph for further comments.
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a reasonable domain for this function would be: 0 <= x <= 40
a reasonable range for this function would be: 280 <= y <= 718
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algebraically, the domain can be 0 <= x <= 80 assuming the maximum number of hours overtime is worked during the week and no weekend work is possible. 5*24 = 120 hours a week minus 40 = 80 hours a week overtime. it's not possible to do more within the 5 days.
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algebraically, the range can be 0 <= y <= 1156 assuming the maximum possible number of hours overtime is worked. the 1156 represents 280 + 80*10.95.
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i chose the reasonable limits with the expectation that no worker would ever work beyond those.
if weekend work were allowed, then the domain and the range would go up accordingly and not be able to go any higher because there would be no more hours available in the week.
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since the equation above is already in slope intercept form (y = m*x + b) where m is the slope and b is the y-intercept, the slope of the equation is 10.95 and the y-intercept of the equation is 280 which is the value of y when x = 0.
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the slope is the change in y value for every change in x value.
in this formula, when x goes up 1, the salary goes up 10.95.
the change in y / the change in x is 10.95/1 = 10.95.
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please note that the x and y values on the graph go below 0. this is only to make the graph show the axes properly and any value where x < 0 or y < 0 should be ignored.
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