Question

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.

Answer 1

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).