Question

How do I find Y for ax+by+c=0

Answer 1

By Y you mean y right?

Answer 2

Yes

Answer 3

Then, to express y in terms of everything else, we have to isolate it on one side of the equal sign while having everything else on the other side of the equal sign. To do this, we use the algebraic operations of adding, subtracting, and dividing to solve for y. It can start like this.\[ax+by+c = 0 \implies ax + by + c +(-c) = -c\].

Answer 4

Since\[c + (-c) = 0 \implies ax + by = -c\]

Answer 5

Now, we can do the same thing for ax.\[(-ax)+ax + by = -(ax) - c \ \implies by = -ax -c\]

Answer 6

Now provided that \[b \neq 0 \], then \[\frac{ by }{ b } = \frac{ -ax -c }{ b } \ \implies y = \frac{ -ax }{ b } - \frac{ c }{ b }\]