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?

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

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?

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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?