Answer: Let x be the number of weeks since Robert started his diet, and let y be his weight in pounds. We know that he is losing weight at a rate of 2 pounds per week, so the slope of the line is -2 (negative because he is losing weight). We also know that after 6 weeks, his weight is 205 pounds, so we have the point (6, 205).
Using the point-slope form of a linear equation, we can write the equation of the line as:
y - 205 = -2(x - 6)
Simplifying this equation gives:
y - 205 = -2x + 12
y = -2x + 217
Therefore, the equation that models Robert's weight loss is y = -2x + 217.
To find how much weight Robert will lose after 8 weeks, we substitute x = 8 into the equation:
y = -2(8) + 217
y = 201
Therefore, Robert will weigh 201 pounds after 8 weeks on his diet.
To check that this answer is reasonable, we can use the information that Robert is losing weight at a rate of 2 pounds per week. In 8 weeks, he would have lost:
2 pounds/week x 8 weeks = 16 pounds
205 pounds - 16 pounds = 189 pounds
Since 201 pounds is more than 189 pounds, our answer of 201 pounds after 8 weeks is reasonable.
So the completed work is:
Let x be the number of weeks since Robert started his diet, and let y be his weight in pounds.
We know that he is losing weight at a rate of 2 pounds per week, so the slope of the line is -2 (negative because he is losing weight).
We also know that after 6 weeks, his weight is 205 pounds, so we have the point (6, 205).
Using the point-slope form of a linear equation, we can write the equation of the line as:
y - 205 = -2(x - 6)
Simplifying this equation gives:
y - 205 = -2x + 12
y = -2x + 217
Therefore, the equation that models Robert's weight loss is y = -2x + 217.
To find how much weight Robert will lose after 8 weeks, we substitute x = 8 into the equation:
y = -2(8) + 217
y = 201
Therefore, Robert will weigh 201 pounds after 8 weeks on his diet.
Explanation: