Find the slope of the line whose equation is 2x-3y+6=0

Answer 1

Rewrite the equation leaving the y term on the left and all other terms on the right, to get: -3y=-2x-6 You can think of this as moving a term to the right and changing its sign, so 2x on the left side becomes -2x on the right side. +6 becomes -6 on the right side. Alternatively or equivalently, take the given equation and subtract 2x+6 from both sides. Now divide by the coefficient of the y term giving y=(-2/-3)x -6/-3 = 2x/3 + 2 or y=(2/3)x+2. This is called the slope intercept form of the linear equation, or y=mx+b where m is the slope and b is the y intercept. b=2/3. The slope of the line is 2/3.

Answer 2

y = mx + b

2x - 3y + 6 = 0

-3y = -2x - 6

-3y/-3 = -2x/-3 - 6/-3

y = (2/3)x + 2

m = 2/3