please help!

Question

To produce 80 copies of a magazine costs 52 cents per copy.
To produce 760 copies of the magazine costs 35 cents per copy.
a) Name two ordered pairs.
b) Write the linear equation.
c) Predict the cost per copy for 480 copies.

Answer 1

From the information, number of copies to be taken as x - coordinate and cost per copy to be taken as y - coordinate.

The ordered pairs are (80, 52) and (760, 35).

Substitute the values of (x₁ , y₁ ) = (80, 52) and (x₂ , y₂ ) = (760, 35) in the slope formula m = (y₂ - y₁) / (x₂ - x₁).

m = (35 - 52) / (760 - 80) = -17/680 = - 1/40.

To write the line equation, we can use either of the two given points.

Consider the point (80, 52).

The point - slope form of the line equation is y - y₁ = m(x - x₁), where m is slope and (x₁ , y₁ ) is point.

m = - 1/40 and (x₁ , y₁ ) = (80, 52).

y - 52 = - 1/40(x - 80)

y - 52 = - 1/40(x) + 2.

y = - (1/40)x + 54.

Substitute x = 480 copies.

Cost y = - (1/40)(480) + 54 = - 12 +54 = 42 cents.

a) The ordered pairs are (80, 52) and (760, 35).

b) The linear equation is y = - (1/40)x + 54.

c) The cost per copy for 480 copies is 42 cents.