1) Egbert charges a fixed rate plus an hourly rate to bill clients. It costs $10

Question

1) Egbert charges a fixed rate plus an hourly rate to bill clients. It costs $100 for a job that is 3 hours of work. This is expressed as an ordered pair (3, 100). a) He charges $190 for 13 hours of work. Express this as an ordered pair. b) Find the slope between these 2 points. What does the slope represent in terms of Egbert's fees? c) Write a linear equation to represent this scenario where x is the number of hours and y is the total charges. d) State the y-intercept: Egbert's fees? What does the y-intercept represent in terms of e) Use the equation to find out how much he would charge for 6 hours of work. f) How many hours would result in a total charge of $172?

Explanation / Answer

SolutionA:

ordered pair=(x,y)

x=13 y=190

(13,190)

Solutionb:

slope of (x1,y1)(x2,y2)

is

m=y2-y1/x2-x1

(x1,y1)=(3,100)

and (x2,y2)=(13,190)

m=190-100/13-3

=90/10

m= 9

slope=9

For an increase of 1 hr egberts fees increases by 9$ since slope=change in y/change inx

=change in costs/change in hrs

SOLUTIONC:

for point(3,100) and slope=9

linear equation is

y-y1=m(x-x1)

y-100=9(x-3)

y-100=9x-27

y=9x-27+100

y=9x+73

slope=9

y intercept=73

Solutiond:

y intercept=73

when there is no work(x=0) amount paid is 73$

  

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