A plumber charges a flat $50 for a home service call plus $10 per 15 minutes of labour. Write an equation for calculating the total charges, C, in terms of the hours of labour, H. If you were to plot a graph of C vs. H, what would be the slope and C-intercept of the line?
The equation would be: 40h+50=C
+50 because that is the flat rate. Then, it asks for the terms to be in hours of labor. 40h because 15*4 is 60 minutes, or, 1 hour. 10*4 because I did 15*4. Solve the rest [slope is y/x or, in this case, c/h. c-intercept is the same thing as y-intercept].
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To write an equation for calculating the total charges, C, in terms of the hours of labor, H, we can use the information provided:
The plumber charges a flat rate of $50 for a home service call, which is the C-intercept, and an additional $10 per 15 minutes of labor. We can express the labor in terms of hours. Since there are 60 minutes in an hour, 15 minutes is equivalent to 15/60 = 1/4 hour.
So, for every 1/4 hour of labor, there is an additional charge of $10. This can be expressed as $10 * (4/1) = $40 per hour.
Therefore, the equation for calculating the total charges would be:
C = $50 + ($40 * H)
In terms of graphing, the slope of the line would be $40, and the C-intercept would be $50.
To write an equation for calculating the total charges, C, in terms of the hours of labor, H, we have to consider the flat fee for a home service call ($50) and the additional charge per 15 minutes of labor ($10).
The flat fee of $50 is not dependent on the hours of labor and can be considered as a constant. The additional charge per 15 minutes of labor can be calculated by dividing the labor time by 15 and multiplying it by $10.
Let's break it down step by step:
1. Calculate the additional charge for labor:
Since every 15 minutes of labor costs $10, the additional charge for labor can be represented as: (10/15) * H.
2. Include the flat fee:
Adding the flat fee of $50, we get the equation for calculating the total charges, C, in terms of the hours of labor, H:
C = (10/15) * H + $50
Now, to determine the slope and C-intercept for the graph of C vs. H, we can rewrite the equation in slope-intercept form, y = mx + b:
C = (2/3) * H + $50
Comparing this equation to y = mx + b, we can see that the slope (m) is (2/3) and the y-intercept (C-intercept, b) is $50.