a young sumo wrestler decided to go on a special high - protein diet to gain weight rapidly. after 11…

a young sumo wrestler decided to go on a special high - protein diet to gain weight rapidly. after 11 months, he weighed 140 kilograms. he gained weight at a rate of 5.5 kilograms per month. let y represent the sumo wrestlers weight (in kilograms) after x months. complete the equation for the relationship between the weight and number of months.

a young sumo wrestler decided to go on a special high - protein diet to gain weight rapidly. after 11 months, he weighed 140 kilograms. he gained weight at a rate of 5.5 kilograms per month. let y represent the sumo wrestlers weight (in kilograms) after x months. complete the equation for the relationship between the weight and number of months.

Answer

Explanation:

Step1: Identify the slope - intercept form

The relationship is linear of the form $y = mx + b$, where $m$ is the rate of change and $b$ is the initial value. The rate of weight gain $m = 5.5$ kg per month.

Step2: Find the initial weight

We know that at $x = 11$ months, $y=140$ kg. Substitute into $y=mx + b$: $140=5.5\times11 + b$.

Step3: Solve for the initial weight $b$

First, calculate $5.5\times11 = 60.5$. Then, $140=60.5 + b$. So, $b=140 - 60.5=79.5$.

Step4: Write the equation

The equation is $y = 5.5x+79.5$.

Answer:

$y = 5.5x + 79.5$