The manager of a furniture factory finds that it costs $2200 to manufacture 100 chairs in one day and $4800 to produce 300 chairs in one day.

If the relationship between cost and the number of chairs produced is linear, how do I write an equation that expresses this relationship?

Step-by-step explanation:

If the relationship between cost and the number of chairs produced is linear, we would write an equation that expresses this relationship in the slope intercept form. It is expressed as

y = mx + c

Where

m represents the slope

c = intercept.

Slope = (y2 - y1) / (x2 - 1)

y2 = final value of y = 4800

y1 = initial value of y = 2200

x2 = final value of x = 300

x1 = initial value of x = 100

Slope, m = (4800 - 2200) / (300 - 100) = 2600/200 = $13 per chair.

To determine the intercept, we will substitute y = 4800, x = 300 and m = 13 into y = mx + c. It becomes

4800 = 13*300 + c = 3900

c = 4800 - 3900 = 900

The equation becomes

y = 13x + 900