Linear Relations Plumbing Companies Question

Question

Two different plumbing companies Bettapipes and Nodrips change according to the following table (closest thing I can do to a table):

Bettapipes: 2 hours | 6 hours
                     $100 | $220



Nodrips: 2 hours | 6 hours
                   $76 | $228


(a) Each company calculates its changes according to a linear formula. For each company, determine the equation relating the total cost of work (C dollars) and the number of hours worked (h)

(b) Describe the way in which each company works out its changes

(c) Which agency offers the better deal for 5 hours work?

Answer 1

The equation of a line may be in Slope-Intercept Form, Standard Form, Point-Slope Form, etc.  Let’s use Slope-Intercept Form:   y = mx + b  (m=slope and b=y-intercept). 

The slope is often called “rise over run,” because it is the increase in the y-values divided by the increase in the x-values.  Here you have two points for each company: 

    For B:  (2,100) and (6,220);  slope=(220-100)/(6-2) = 120/4 = 30

    For N:  (2,76) and (6,228); slope=(228-76)/(6-2) = 152/4 = 38

 

Plug in either point to find the y-intercept for each line:

 For B: y = 30x + b;  100=30(2)+b;  b=40    so, y=30x+40

 For N: y= 38x + b;  76=38(2)+b;  b=0   so, y=38x

 

(a) In terms of C and h, this is:

   For B:   C=30h+40          [has points (2,100) and (6,220)]

   For N:   C=38h               [has points (2,76) and (6,228)]

 

(b) Company B has an initial charge of $40 and then $30 for each hour of work.  Company N just charges $38 for each hour of work.

 

(c)  At h=5,

      Company B charges  C=30h+40  =  30(5)+40  =  150 + 40  = $190

      Company N charges  C=38h =  38(5)  =  $190

 

  At 5 hours of work, the two companies charge the same amount.