SOLVING FOR Y: How to Pull a Clooney
When you guys have an equation of a line in Standard Form like
3x – 5y = 15
and you have to change it into Slope-Intercept Form so that it looks like
y = 3/5x – 3
we often get asked: what do you do first?
The answer: Pull a Clooney.
You see, in Slope-Intercept form, “y” is like George Clooney: a modern-day lothario who prefers to travel solo. Clooney has a reputation of being in relationships which inevitably end, and such is also the fate for any y relationship. Yet, Clooney has class. Have you ever seen Clooney publicly break up with any of his exes? No. And we don’t think the obligatory demise of Keibler/Clooney will be any different. Your job when isolating y is to pull a Clooney: get everyone else out of the room, then break it off.
Before we show you how to do this mathematically, here’s a piece of visual interest:
GUYS: THIS IS WHAT CLOONEY USED TO LOOK LIKE!!! AHAHAHAHAHAHAHA! THERE’S HOPE FOR US ALL! (Note to everyone: your dorky lab partner could very well grow up to be a silver fox so BE NICE.)
So you have 3x – 5y = 15. You’ve gotta get y alone.
Imagine that 3 and x are dating and 5 and y are dating. y wants to break up with 5 but he’s not gonna do it in front of 3 and x because that would be awkward and insensitive. So the first step is to get 3 and x out of the room. They’re happy, they’re staying together. They don’t need to be here for this.
Subtract 3x from both sides of the equation. Remember, to move something to the other side of an equal sign, you have to do the opposite operation of what it’s already doing. Since 3x doesn’t have a – sign in front of it, it’s positive, which is like it’s being added to the left side of the = sign. So you’re gonna move it by subtracting 3x from the left. And in Algebra, whatever you do to the left you have to do to the right. So then also subtract it from the right.
Now you’ve got: -5y = -3x + 15
Ok, now for the break-up.
George Clooney The letter y is now alone with Stacy Keibler the number 5 (well, actually -5, since there’s a minus sign there). y is all ready to drop -5 like it’s hot. To make that happen, divide the left side by -5. Remember: move something by doing the opposite operation. -5 is mathematically glued to y by multiplication, so the opposite of that is division. Since you’re dividing the left side by -5, you’ve got to divide everything on the right side by -5. Which gives you:
-5y/(-5) = -3x/(-5) + 15(-5)
And then that gives you: y = -3/5x + (-3) or y – -3/5x – 3.
Tada! y is successfully alone. And thank god, because he’s gotta go hang out with Clooney at the hotel bar and find his next conquest.