SOLUTION: how do i find the slope and y-intercept of x-3y=18?

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Question 546791: how do i find the slope and y-intercept of x-3y=18?
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
You can change the equation to the form that starts with "y=..." That form is called the slope-intercept form for good reason. Let me show you.
You start with x-3y=18 and try to solve for y.
You could add 3y to both sides, then subtract 18 from both sides, then divide both sides by 3:
x-3y=18 ---> x=3y%2B18 ---> x-18=3y --->%281%2F3%29x-6=y
Or you could say you'll subtract x from both sides, then divide by %28-3%29:
x-3y=18 ---> -3y=18-x ---> y=%281%2F3%29x-6
You may even think of another way.
Of course, the result is the same.
Unless you made a mistake, you get y=%281%2F3%29x-6.
You clearly see the number %281%2F3%29 multiplied by x, and that is the slope, because as x increases by 1, y increases by that number, the slope, %281%2F3%29.
You also see that when x=0, which is at the y-axis, y takes the value of the number that is added to the %281%2F3%29x. That is the value of y when the line crosses the y-axis, the y-intercept, -6 in this case.
So you see how the slope-intercept form clearly shows you the slope (multiplied times x), and the intercept (the rest of the equation). It is very useful, and as wonderful as Tigger, because there is only one slope-intercept form.