Answer: p = -4.5w+268
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Step-by-step 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.