Put the following equation of a line into slope-intercept form, simplifying all fractions.
3x-6y=-30
To convert the equation 3x-6y=-30 into slope-intercept form, we want to solve for y and rewrite the equation in the form y = mx + b, where m is the slope and b is the y-intercept.
Starting with the given equation:
3x - 6y = -30
First, we can simplify the equation by dividing every term by the common factor of 3:
(3x - 6y)/3 = (-30)/3
Simplifying further:
x - 2y = -10
Now, we isolate the term with y by subtracting x from both sides of the equation:
x - 2y - x = -10 - x
Simplifying and rearranging:
-2y = -x - 10
To get y by itself, we divide every term by -2 (this step changes the sign of both terms):
(-2y)/(-2) = (-x)/(-2) - 10/(-2)
Simplifying further:
y = (1/2)x + 5
Thus, the equation 3x-6y=-30 in slope-intercept form is y = (1/2)x + 5.