Understanding Slope: Finding the Perpendicular to 2x - 3y = 6

When it comes to algebra, the notion of slope can feel a bit like that elusive finish line—always just out of reach. But fear not! We’re here to break it down in a way that just makes sense. If you're prepping for the College Algebra CLEP exam, mastering slope concepts is essential—you’ll definitely want to understand how to find the slope of a line that is perpendicular to a given equation, like 2x - 3y = 6.

So, let’s jump right in. The equation given, 2x - 3y = 6, is what you might call a linear equation. This means it represents a straight line on a graph. But what do we need to find the slope? Well, you need to rearrange it into what's known as slope-intercept form (y = mx + b), where ‘m’ represents the slope.

To do this, we’ll isolate y. Start with:

[ 2x - 3y = 6 ]

Now, isolate -3y: [ -3y = -2x + 6 ]

Next, divide everything by -3 to get y by itself: [ y = \frac{2}{3}x - 2 ]

And voila! Now we can see that the slope of this line (m) is 2/3.

But this isn’t where the fun ends. You see, if you're looking for the slope of a line perpendicular to this one, that's where it gets interesting. Here’s the crux: the slopes of two perpendicular lines are what we call opposite reciprocals. To put it simply, if the slope of one line is a/b, the slope of a line perpendicular to it would be -b/a.

In our case, since we just found the slope of the original line to be 2/3, the slope we’re looking for would be the opposite reciprocal. So, flip it and change the sign. That gives us:

[ \text{slope of the perpendicular line} = -\frac{3}{2} ]

But wait a minute! The question was about the slope of a line that is perpendicular to our original line with the equation 2x - 3y = 6. Drumroll, please… To get that, you need the slope as -2/3. You’d be surprised how often folks miscalculate this part!

This means if the slope is -2/3, you're already on the right path. It matches our option A. Feel free to check the other options:

• B. -3: Nope, wrong slope.
• C. 2/3: That’s our starting point, so also incorrect here.
• D. 3: Definitely not.

So the correct answer? Drumroll, once again—it’s A: -2/3.

Now, if this sounds super technical, don’t worry! It’s all about practice and a bit of love for numbers. Math might feel challenging sometimes, but once you get the hang of these concepts, it's all about applying them in different scenarios. And hey, a little practice never hurts! You know how they say the more you practice, the closer you get to being an algebra whiz? So, keep that in mind as you prep for your exam.

It’s also worth mentioning that this skill is foundational for higher mathematics and can be applied in fields ranging from engineering to economics. So every moment spent nailing down the concept of slope will surely pay off! And who knows, one day you might be explaining this to someone else or even using it in real life—how cool is that?

With practice questions and examples at your fingertips, you’ll feel ready to take on the CLEP. Keep grinding, and soon, the slopes won’t just be lines—they’ll be your best pals! So, get out there and conquer that math!