Word problem

Question

It costs XYZ Corporation $8500 to produce 1400 units and $5380 to produce 200 units. Let represent the cost in dollars and represent the number of units produced. Find a linear equation for in terms of .

Answer 1

Let y = cost and x = units produced

 

The equation of a line is y = mx + b where m = the slope of the line and b = the y-intercept.  To find the equation of a specific line, we need to find the values of m and b.  We have two points: (1400,$8500) and (200,$5380).  The slope is the change in the y-values between the two points over the change in the x -values:

 

m = (change in y)/(change in x) = (8500-5380)/(1400-200) = 3120/1200 = 2.6

 

So m = 2.6 and the equation of our line so far is:

 

y = 2.6x + b

 

To find b, plug in the x and y values from either of the given points and solve for y.  I'll use (200,5380):

 

5380 = 2.6*200 +  b

5380 = 520 + b

4860 = b

 

So the equation of our line is:

 

y = 2.6x + 4860