Question

A construction company charges $15 per hour for debris removal, plus a one-time fee for the use of a trash dumpster. The total fee for 9 hours of service is $195.

a. Write the point-slope form of an equation to find the total fee y for any number of hours x.
b. Write the equation in slope-intercept form.
c. What is the fee for the use of a trash dumpster?

Answer 1

The point-slope form of the equation for the total fee y for any number of hours x is y - 195 = 15(x - 9). The equation in slope-intercept form is y = 15x + 60, and the one-time fee for the use of a trash dumpster is $60.

Step-by-step explanation:

The construction company's total fee y for any number of hours x can be expressed using the point-slope form equation:

y - y1 = m(x - x1)

where m is the slope (rate of charge per hour) and (x1,y1) is a point on the line. Given that the total fee for 9 hours is $195 and the per hour charge is $15, we can say that:

m = $15/hour

and (9, 195) is a point on the line, so:

y - 195 = 15(x - 9)

In slope-intercept form, this equation would be:

y = 15x + b

Using the given point (9, 195) to solve for b, we find that:

195 = 15(9) + b

Thus, b = 195 - 135 = $60, which is the one-time dumpster fee. Therefore, the slope-intercept form of the equation is:

y = 15x + 60.