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A company in its first year of business produced 1,200 brochures for a total cost of $5,050. The following year, the company produced 500 brochures at a cost of $2,250. Use this information to find a linear function that gives the total cost of producing brochures from the number of brochures produced.
Use x and y for the independent and dependent variables.

Respuesta :

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Think of 2 points, (1200,$5050) and (500,$2250), on a straight line.  Find the slope and y-intercept of this line:

        5050-2050       3000
m = ---------------- = ----------- = 30/7
         1200-500          700

Now let's write out the slope-intercept form of the equation of a straight line:

y = mx + b.  Substituting 30/7 for m, 500 for x and 2250 for y, we get:

2250 = (30/7)(500) + b.  This can be solved for b:  b = 107.14 (or 750/7).

Then the linear function is   y = (1/7)(x + 750).