Question

A young sumo wrestler decided to go on a special high − -protein diet to gain weight rapidly. After  1 1 11 months, he weighed  1 4 0 k i l o g r a m s . 140 kilograms. He gained weight at a rate of  5 . 5 k i l o g r a m s 5.5 kilograms per month. Let  y y represent the sumo wrestlers weight ( i n k i l o g r a m s ) (in kilograms) after x months. Whats the y-intercept?

Answer 1

Given:

After 11 months, sumo wrestler weighed 140 kilograms.

He gained weight at a rate of 5.5 kilograms per month.

To find:

The y-intercept of the equation which represents y the sumo wrestlers weight (in kilograms) after x months.

Solution:

Let y represent the sumo wrestlers weight (in kilograms) after x months.

It is given that he gained weight at a rate of 5.5 kilograms per month.

So, slope of the line is 5.5.

After 11 months, sumo wrestler weighed 140 kilograms. It means the line passes through the point (11,140).

The point slope form of the line is

`y-y_1=m(x-x_1)`

where, m is slope of the line.

`y-140=5.5(x-11)`

`y-140=5.5x-60.5`

Add 140 on both sides.

`y-140+140=5.5x-60.5+140`

`y=5.5x+79.5`

Therefore, the required equation is
`y=5.5x+79.5`.

Substitute x=0, to find the y-intercept of this equation.

`y=5.5(0)+79.5`

`y=79.5`

Therefore, the y-intercept is 79.5. It means initial weight of sumo is 79.5 kilograms.