## Other Line Equation Methods

### Algebra: Lines Help

It doesn't get any easier than this.

Let's examine the facts.

The general equation is y = mx + b. There are 4 variables, right?
You are given a point - that takes care of x and y.
If you are given the slope, that takes care of m.
Or, if you are given the y-intercept, that takes care of b.

So, all you do is plug your 3 numbers into the equation and solve for the 4th number. If you need help solving for the last number, you might want to go to the Solve for x index and check out the help pages you need.

What if the problem gives you a point and says the line you want is parallel or perpendicular to another line?
Guess what? They're giving you the slope for your line. Granted, you might have to use your brain for a few seconds to figure it out, but you don't have to be a nuclear physicist to find it. All you have to do is get the equation into the y = mx + b form. Let's trudge through a few examples.

Example 1: Your line is parallel to y = -6x - 23. The slope of the other line is -6. Ergo, the slope of your line is -6.

Example 2: Your line is parallel to 2y = 3x - 4. First we divide everything by 2 so we get the equation into the y = mx + b form. Once we do that, we see that the slope is 3/2.

Example 3: Your line is parallel to 2x - 3y = 6. We have two steps here to get the equation into the proper form. Step 1: Subtract 2x from both sides. Now our equation is -3y = -2x + 6. Then just like in example 2, we divide everything by -3 to get the equation in the proper form. Once we do that, we find the slope = 2/3.

If the other line is perpendicular to your line, what you do is find the slope of the other line, then use the negative reciprocal as the slope for your line. That's a fancy way of saying you take the reciprocal of the slope and multiply it by -1.

Example 4: Find the equation of a line perpendicular to 2x - 9y = 6.
First, we find the slope of this line the same way we did in example 3. We get the slope = 2/9. The negative reciprocal of this is -9/2. That is the slope of your line.