Question

A yearbook printer charges based on the number of pages printed. Here is a table that shows the cost of some recent yearbooks.

Number of pages 50 100 150 200
Cost 1.25 2.55 3.85 5.15

Which equation gives the cost, y, in terms of the number of pages, x?

y = 0.026x + 49.15

y = 0.026x + 1.25

y = 0.026x – 0.05

y = 58.8x + 0.95

Answer 1

Option C.

Explanation:

Let y is the cost of recent yearbooks and x is the number of pages.

If a line passes through two points
`(x_1,y_1)` and
`(x_2,y_2)`, then the equation of line is

`y-y_1=(y_2-y_1)/(x_2-x_1)(x-x_1)`

Choose any two ordered pairs from the giver table.

Consider the line passes through the points (50,1.25) and (100,2.55). So, the equation of line is

`y-1.25=(2.55-1.25)/(100-50)(x-50)`

`y-1.25=(1.3)/(50)(x-50)`

`y-1.25=0.026(x-50)`

Using distributive property, we get

`y-1.25=0.026(x)+0.026(-50)`

`y-1.25=0.026x-1.3`

Add 1.25 on both sides.

`y-1.25+1.25=0.026x-1.3+1.25`

`y=0.026x-0.05`

The equation of line is y=0.026x-0.05. Therefore, the correct option is C.

Answer 2

y = 0.026x – 0.05

Explanation:

When the number of pages increases by 100, the cost goes up 2.60, so the price per page is 0.026, and the cost for x pages is 0.026x.

For the first 50 pages, the cost is only 1.25, which is less than 1.30 by 0.05, so the cost function is ...

... y = 0.026x - 0.05