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Bill began his diet when he weighed 268 pounds. After 4 weeks he weighed 250 pounds. Write an equation in slope-intercept form of the line if w represents weeks and p represents pounds

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Answer:      p = -4.5w+268

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Explanation:

For now, I'll use x to represent the number of weeks and y to represent Bill's weight for week x.

He starts off at 268 pounds. This means week x = 0 corresponds to the weight y = 268 points. In short, the point (0,268) is on the line.

Similarly, the point (4,250) is also on the line telling us that at week x = 4, his weight has dropped to 250 lbs.

Let's find the slope of the line through these two points

m = (y2-y1)/(x2-x1)

m = (250-268)/(4-0)

m = -18/4

m = -4.5

The slope is -4.5; it means that each week, Bill has lost 4.5 pounds (aka every 2 weeks, he loses 9 pounds).

Because Bill started at 268 pounds, this is the y intercept b value. So b = 268

The slope intercept form y = mx+b will then update to y = -4.5x+268

The last task is to replace x with w, and replace y with p

That's how we arrive at the final answer:  p = -4.5w+268

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If we tried w = 4, to represent 4 weeks, then we get

p = -4.5*4+268

p = -18+268

p = 250

which helps confirm we have the correct equation.