How and why do you do this

Question

Ok so, I'm doing Khan Academy and I got stuck on this question.

-x/3.5 + y/12.5 = 1

On the khan, it just put 12.5 on top of the -x/3.5 and it makes it -12.5/3.5 x. I just understand why and how this works. Please help me. Oh yeah, almost forgot, I doing this on the SAT dashboard on Khan.

Answer 1

They did not just "put" it on the numerator. They multiplied both side of the equation by 12.5

-x/3.5 + y/12.5 = 1

-12.5x/3.5 + 121.5y/12.5 = 12.5(1)

-12.5x/3.5 + y = 12.5

Answer 2

There is no math problem here. Are you solving for y in terms of x?

The normal thing to do is to multiply through by 3.5*12.5 in order to get rid of the fractions:

-12.5x +3.5y = 3.5*12.5

solving for y, you get

y = 12.5 + (12.5/3.5)x

If you were trying to find the slope, that is clearly 12.5/3.5 in the mx + b form that I derived.

You can also just pick off the slope from the

ax + by = c form as -a/b here a = -1/3.5 b = 1/12.5