Express the​ cost, y, as a linear function of the number of​ heaters, x. Determine the cost to produce 20 heaters

Question

A company finds it can produce 5 heaters for $2000, while producing 10 heaters costs $3300. Express the​ cost, y, as a linear function of the number of​ heaters, x. Determine the cost to produce 20 heaters.

Express the​ cost, y, as a linear function of the number of​ heaters, x.

y=__

The cost to produce 20 heaters is $__

Answer 1

First find the slope (m in the linear equation y = mx + b)

(y_{2 -} y₁)/(x₂ - x₁) that's rise over run

(3300 - 2000)/(10 - 5) = 1300/5 = 260

y = 260x + b.

Now need to find b (y-intercept). Use either pair: Ex: 3300 = 260(10) + b

b = 3300 - 2600 = 700.

So y = 260x + 700

For 20 heaters: y = 260(20) + 700 = 5200 + 700 = $5,900.

Answer 2

Start with two-point form from Algebra 1.

(y - 2000) / (x - 5) = (3300 - 2000) / (10 - 5)

Perform operations and convert to slop-intercept form.

Substitute x = 20 and solve for y.