Question

How do I solve this -4y+x=-27

Answer 1

According x variable;

$-4y+x=-27\\ \\ \boxed{x=4y+27}$

According y variable:

$-4y+x=-27\\ \\ -4y=-27-x\\ \\ \boxed{y=\frac{-27-x}{-4}}$

Answer 2

First you have to know what a "solution" is.

The 'solution' is a set of 2 numbers which, if you put them into the equation
in place of 'x' and 'y', make the equation a true statement. 

There are an infinite number of possible pairs of numbers that can do that. 
Here are a few:

x = 0, y = 6.75 
x = 1, y = 7
x = 2, y = 7.25
x = 3, y = 7.5
x = 4, y = 7.75
x = 10, y = 9.25
x= 100, y = 31.75
x= -50, y = -5.75

When you graph this equation, the graph is a straight line without any ends.
Every point on the line is a solution to the equation, and you know how many
points there are on a line without ends . . . . .