Put the following equation of a line into slope-intercept form, simplifying all fractions.

Question

3x+6y=36

Answer 1

To put the equation 3x + 6y = 36 into slope-intercept form, we need to solve for y.

Starting with the given equation:
3x + 6y = 36

We can begin by isolating y on one side. To do so, we can subtract 3x from both sides:
6y = -3x + 36

Next, we can further isolate y by dividing both sides by 6:
(6y)/6 = (-3x + 36)/6

This simplifies to:
y = (-3/6)x + 6

Now, to simplify the fraction (-3/6), we can divide both the numerator and denominator by their greatest common divisor, which is 3:
y = (-1/2)x + 6

Thus, the equation 3x + 6y = 36 is simplified to y = (-1/2)x + 6 in slope-intercept form.