Question

A scientist discovers a new way to produce vitamin C. In 15 hours, 678 kilograms are produced. In 25 hours, 1018 kilograms are produced. Write an equation in the form of y = mx + b for how many kilograms, y , are produced in x hours.

Answer 1

The equation of the line is
`y = 34\cdot x + 168`.

Explanation:

According to Analytical Geometry, we know that any equation of the line can be determined by knowing two distinct points on Cartesian plane. From statement we get that:

`y(15\,h) = 678\,kg` (1)

`y (25\,h) = 1018\,kg` (2)

By applying the definition of the equation of the line, we form this system of two linear equations with two variables:

`15\cdot m + b = 678` (3)

`25\cdot m + b = 1018` (4)

By algebraic mean we get the following solution:

`m = 34\,(kg)/(h)` and
`b = 168\,kg`

And the equation of the line is
`y = 34\cdot x + 168`.