Mastering Line Equations: A Key Skill for Your College Algebra Journey

When it comes to mastering algebra, understanding how to find the equation of a line is a crucial skill. Whether you're gearing up for your college algebra classes or preparing for the College Algebra CLEP exam, knowing how to tackle these problems can save you from many late-night study sessions. Let’s break down the process step-by-step.

You might remember from your math classes that the slope-intercept form of a line is expressed as y = mx + b. Here, m represents the slope, while b is the y-intercept. But what does this mean for you? Essentially, you need to grasp how these elements fit together to find the equation of a line.

So, let's consider a problem that exemplifies this. You need to find the equation of a line with a slope of 2/3 that passes through the point (-3, 5). Okay, take a deep breath; this is where it gets fun!

First off, let’s plug those values into our precious slope-intercept formula. The equation starts looking like this:

y = (2/3)x + b

Now, here’s the trick. We need to find b. To do this, we’ll use the coordinates provided: the x-coordinate is -3 and the y-coordinate is 5. By substituting these values into our equation, we can find our elusive y-intercept.

5 = (2/3)(-3) + b

Now, let's do some quick calculations. What’s (2/3)(-3)? That's -2. So, we have:

5 = -2 + b

Now, here’s a little algebra magic: if we add 2 to both sides, we get:

b = 7

Aha! Now we’ve got our y-intercept. Thus, we can merge everything back into the equation, making it:

y = (2/3)x + 7

And voila! Here we have it: our beloved equation of the line. This means that the correct answer to our problem is B: y = 2/3x + 7.

But what about the other choices? Let’s briefly dissect them for clarity's sake.

• A: y = -2/3x + 10 – Look at that slope! It’s negative, not matching ours. Next!
• C: y = 2/3x - 5 – Close, but the intercept is off. You need that extra +7 back.
• D: y = -2/3x - 5 – Once again, it’s negative. Let’s drop that one too.

Now that you've navigated through this problem, you're well on your way to mastering not just this type of question but many others you'll face.

But why stop here? There’s a whole world of algebra waiting for you, from quadratic equations to graphing functions. As you delve into these topics, stay curious. Maybe even reflect on how math connects to real-world scenarios, like determining the trajectory of a basketball or optimizing profits in business!

So gear up, keep practicing, and don’t hesitate to tap into resources, practice exams, and perhaps even study groups. Do you see how grounds like finding the slope can ripple through your algebra studies? Keep pushing forward, and you’ll find that mastering these skills makes a world of difference in your academic journey.