6y = 4x+36
y = 2/3 x + 6
slope intercept form
y = 2/3 x + 6
y=-2/3x+6
Step 1: Isolate the y-term.
- Start by subtracting -4x from both sides of the equation: -4x + 6y - (-4x) = 36 - (-4x).
Simplifying, we get: 6y = 4x + 36.
Step 2: Divide by the coefficient of y.
- Divide both sides of the equation by 6 in order to isolate y: (6y) ÷ 6 = (4x + 36) ÷ 6.
This simplifies to: y = (4/6)x + 6.
Step 3: Simplify the fraction (4/6).
- The fraction 4/6 can be reduced to 2/3 by dividing both the numerator and denominator by their greatest common divisor, which in this case is 2.
Therefore, the final equation in slope-intercept form is: y = (2/3)x + 6.
Let's begin by moving the -4x term to the other side:
-4x + 6y = 36
Move -4x to the right side by adding 4x to both sides:
6y = 4x + 36
Now, divide both sides of the equation by 6 to solve for y:
y = (4/6)x + 36/6
Simplify the equation:
y = (2/3)x + 6
So, the equation -4x + 6y = 36, when rewritten in slope-intercept form, becomes y = (2/3)x + 6. The slope is 2/3, and the y-intercept is 6.