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.