Nguyen's New Year''s resolution was to lose weight.

Question

at the beginning of the new year nguyen weighed 314 pounds after 128 days she weighed 218 pounds. find the rate of change of weight loss over time and wrtie a linear equation modeling nguyen's weight loss

Answer 1

We need to begin by defining our variables, so we can find our equation.  We can define x as the number of days into the year and y as Nguyen's weight.  Using these variables, we can come up witht the points (0,314) and (128, 218).

The slope formula states: m = (x₂ - x₁)/(y₂ - y₁)

Substituting our values, we have m = (218 - 314)/(128 - 0)

m = -96/128

which reduces to m = -3/4

The slope is the rate of weight loss, so Nguyen lost 3/4 of a pound per day.

To find the equation, we need to plug the slope and one of our points into the point slope formula.  I recommend using the point (0,314) because one of the values is 0.

Point-slope formual is y - y₁ = m(x - x₁)

Substituting our values, we have y - 314 = -3/4(x - 0)

y - 314 = -3/4x

y = -3/4x + 314

 

Answer 2

Let's notice 2 things right away. First, the question asks for a LINEAR equation so that means we want the equation of a LINE.  What's the universal equation of a line?  It's y=mx + b, where m is the slope and b is the y-intercept. Next we see that Nguyen's weight is DECREASING, so the slope must be NEGATIVE.

Ok, we now have all we need to answer this. First the let's get the slope. Remember the catchy phrase "rise over run"? Well, in this case it's "drop over run". His weight drops from 314 to 218. That's a difference of 96 pounds in the NEGATIVE direction. The "run" in this case is the time it took to lose the weight, which is 128 days. So the SLOPE is -96/128 or -0.75 on your calculator.

So, plugging that into our universal formula we have y = -0.75x + b.  But what is b? Well, when x = 0 then y = b.  At day 0 Nguyen weighed 314 lbs.  So, b = 314.

So, then the whole equation is y = -0.75x + 314.  Nguyen can now calculate how long it will take him to lose any amount of weight he wants.  But if he loses too much he may not live long enough to get to his desired weight.