Question 78563
2x-3y=6

Since 2x does not contain the variable to solve for, move it to the right-hand side of the equation by subtracting 2x from both sides.
-3y=-2x+6

Divide each term in the equation by -3.
-(3y)/(-3)=-(2x)/(-3)+(6)/(-3)

Simplify the left-hand side of the equation by canceling the common terms.
y=-(2x)/(-3)+(6)/(-3)

Simplify the right-hand side of the equation by simplifying each term.
y=(2x)/(3)-2

To find the slope and y intercept, use the y=mx+b formula where m=slope and b is the y intercept.
y=mx+b

Using the y=mx+b formula, m=(2)/(3) and b=-2.
m=(2)/(3), b=-2