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A young sumo wrestler decided to go on a special high-protein diet to gain weight rapidly and at a constant rate. After $8$ months, he weighed $138$ kilograms. He started at $90$ kilograms.Let $y$ represent the sumo wrestler's weight (in kilograms) after $x$ months. $\newline$ Complete the equation for the relationship between the weight and number of months. $\newline$ $y=\square$

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Write a linear function: word problems

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Q. A young sumo wrestler decided to go on a special high-protein diet to gain weight rapidly and at a constant rate. After

8

months, he weighed

138

kilograms. He started at

90

kilograms.Let

y

represent the sumo wrestler's weight (in kilograms) after

x

months.

\newline

Complete the equation for the relationship between the weight and number of months.

\newline

y=\square

Determine rate of weight gain: Determine the rate of weight gain per month. $\newline$ The sumo wrestler started at $90$ kilograms and weighed $138$ kilograms after $8$ months. To find the rate of weight gain per month, we subtract the starting weight from the weight after $8$ months and divide by the number of months. $\newline$ Rate of weight gain per month = (Weight after $8$ months - Starting weight) / Number of months $\newline$ Rate of weight gain per month = $(138 \, \text{kg} - 90 \, \text{kg}) / 8 \, \text{months}$ $\newline$ Rate of weight gain per month = $48 \, \text{kg} / 8 \, \text{months}$ $\newline$ Rate of weight gain per month = $6 \, \text{kg/month}$
Calculate weight after x months: Write the equation for the sumo wrestler's weight after x months. $\newline$ We know that the wrestler gains $6$ kilograms each month. Therefore, the weight after $x$ months can be calculated by starting with the initial weight and adding $6$ kilograms for each month that passes. $\newline$ $y = \text{Initial weight} + (\text{Rate of weight gain per month} * \text{Number of months})$ $\newline$ $y = 90 \, \text{kg} + (6 \, \text{kg/month} * x)$
Simplify the equation: Simplify the equation. $\newline$ The equation from Step $2$ is already in its simplest form, so no further simplification is needed. $\newline$ $y = 90 + 6x$

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