how to find the cost per month of producing a lamp

Question

A company has a manufacturing plant that is producing quality lamps. They find that in order to produce 290 lamps in a month, it will cost $9530. Also, to produce 500 lamps in a month, it will cost $15200. Find an equation in the form y=mx+b,y=mx+b, where x is the number of lamps produced in a month and y is the monthly cost to do so.

Answer 1

 x is the number of lamps and y is the cost so we have two points that fit on the line

Point 1: (290, 9530)

Point 2: (500,15200)

to find an equation you need to figure out the slope (m) which is the cost per lamp and the y-intercept (b) which is the base costs eg:cost of equipment

 

to find the slope use the equation:

m=y₂-y₁

     x₂-x₁

plug in your numbers: 15200-9530 = 27

                                   500-290   

so now that you have your slope you have to find your y-intercept.  Plug your slope into the equation

y=27x+b

since you have two points you know work you can plug one of them in to find b.

If we use the first point:

9530=27(290)+b

9530=7830+b

1700=b

 

so now that you have m and b you can write an equation

y=27x+1700