10. It takes a machine 12 minutes to fill 200 bottles of soda. At this rate, how many minutes will it take the machine to fill 500 bottles of soda?

30 minutes.

Step-by-step explanation:

Because it takes 12 minutes to fill 200 bottles of soda. Add 12 to 12 again and you'll get 24. In 24 minutes, it'll be 400 bottles. Half of 12 is 6 and half of 200 is 100. So that add 6 minutes (which is a 100 bottles) and you'll get 500 bottles of soda in 30 minutes.

step-by-step explanation:

i think something is missing in your question because y-1=(x-12) would not pass through the point (-4,-3). because if you replace x by -4 your are supposed to find y=-3 which is not the case her. if you replace x by -4 you find =-15.

i assume the right equation is y-1=1/4*(x-12) because this one is passing through both your points (if you are interested to know how i found that out i can tell you).

in this equation if i replace x by -4 i find y=-3 and if i replace x by 12, i find y=1 so the line representing this equation is passing through those 2 points.

then the standard form of the equation is finding an expression of y in function of x

y-1=1/4*(x-12)

y=x/4-3+1

y=x/4-2

hope that .

do you confirm there was a mistake in the question?