What do I do when a number has two variables

Question

4xy-2x^2=3x

So for the 4xy, what do I do?

Answer 1

solve for y

4xy= 2x^2 + 3x

4y =(2x^2+3x)/x = 2x + 3

y = x/2 + 3/4

It's a straight line with slope = 1/2 and y intercept = 3/4

but it's also a vertical line with undefined slope, x=0

if x is zero, y takes on any value

the 2 lines intersect at (0,3/4)

another way to look at it is

take the equation 4xy-2x^2= 3x and set it equal to zero and factor

2x^2 + 4xy -3x = 0

x(2x+4y-3) = 0

set each factor =0

x=0 and

2x+4y-3 = zero, solve for y

y=-x/2 +3/4

that gives you 2 lines