Question

You have a bottle with a leak. After 2 seconds, there are 28 ounces left in the bottle. After 6 seconds, there are 20 ounces left in the bottle. How much water is in the bottle initially

Answer 1

Answer:

32 oz

Step-by-step explanation:

Assuming the hole in the bottle is not made any bigger as it loses water, it will lose it at a constant rate.  This makes it a linear function.  We can use the 2 points given to find the slope of the line, then use one of the 2 points to write an equation for the line in point-slope form, change it into slope-intercept form, and the amount of water in the bottle originally will be apparent.  Plugging in to the slope formula:

$m=\frac{20-28}{6-2}=-2$

Now we will choose one point for the x and y values and plug in to the point-slope form of a line:

y - 28 = -2(x - 2) and

y - 28 = -2x + 4 so

y = -2x + 32

That is in y = mx + b form where m is the slope and b is the y-intercept, the initial value of y when x = 0.  x being the time gone by, when x = 0, that means that no time has gone by, and that means that no water has yet to leak out of your bottle.