Math word problem question

Question

compuwork, a computer repair company, charges a fee and an hourly charge. After two hours, the repair bill is $130, and after five hours it is $250. Write an equation in slope intercept form to describe the relationship between the hour and the cost. What do the slope and y-intercept mean? How much would it cost for 2.5 hours of work? Show or explain how you got your answer.

1. To write an equation in slope intercept form

a. step1 Find the slope

 

b. Step2: Write the equation in point slope form

y-y1=m(x-x1)

 

 

c. step 3: Write the equation in slope-intercept form

y=mx+b

 

2. The slope means...

 

3. The y intercept means...

 

4: For 2.5 hours of work it would cost..

 

Answer 1

I will tell you how to find the point-slope form.

It will be good to exercise your understanding by answering the rest by yourself!

 

The equation you seek must pass through (2,130) and (5,250); hence the slope is

 

m = (250-130)/(5-2) =120/3 = 40 (BTW this is the hourly rate!)

 

The equation then is B  = 40h + f where B= the bll amount, h is the # of hours worked and f is the flat fee.

 

You should be able to do the rest from here, but if not, please send me a message so that I can provide further help.

 

f is determined from 130 = 40 * 2 + f  => 130 = 80 + f => f = 50

 

Finally your slope intercept form is B = 40h + 50.

Answer 2

1. To write an equation in slope intercept form
a. step1 Find the slope

 

The slope is the cost per hour:     

     The problem gives the points:    (2,130)  and   (5,250)

       This is a rate of (250-130)/(5-2) or 120/3 = $40/hr

 

b. Step2: Write the equation in point slope form

y-y1=m(x-x1)
      y - 130 = 40(x-2)            [use either point]

c. step 3: Write the equation in slope-intercept form
y=mx+b
      y = 40x - 80 + 130

      y = 40x + 50

2. The slope means...
        The Unit Rate in dollars per hour.

3. The y intercept means...
        The base charge for zero hours.

 

4: For 2.5 hours of work it would cost..

         y = 40x +50

         y = 40(2.5) + 50

         y = 100 + 50

         y = $150