INSTRUCTOR: Welcome to friendly math 101. Today's lesson is over parallel lines. We're going to write equations of parallel lines. So let's start by talking about, what is a parallel line? Parallel lines are lines that will never intersect. 

So when we're looking at an equation in the form y equals mx plus b, parallel lines are going to have the same slope. So the m is going to be the same in parallel lines. But they have different y-intercepts, so different b values. If they had the same slope and the same b value, it would be the same line, so they would not be parallel. So that's very important-- the same slope, the same m, but different b values. 

So let's start our first examples. We're going to list a parallel slope. So first, we want to look at the slope of the line and then find a slope parallel to that. So number 1, y equals mx plus b. Our slope is our m. And our m here is this 5. That's our slope of this line. So a parallel slope would be the same slope. So our answer would actually just be a slope of 5. 

Number 2, y equals 3/4 x plus 7. Again, we're looking for the slope. Here, it's 3/4. We want a parallel slope. That would be the same slope. So our answer is 3/4. Number 3, we're looking for slope y equals x. There is no m value. There is an x, though. So it's actually a understood 1 in front of that x. So our slope is actually 1 here, meaning our parallel slope is also 1. 

So those are our answers to those questions. Our next example says to write an equation parallel to y equals 1/2 x minus 3. Remember, we need the same m but a different b. So as I'm writing this equation, I want the same m. So it's going to be 1/2 x. 

But I want a different number here. It can be any number other than negative 3. So I'm going to put plus 2. Again, it doesn't matter. So there are an infinite number of answers because the b can be any value except for negative 3. But this is the answer that I've chosen. 

Here's another one. We're going to write an equation parallel to this line here, y equals negative 3x plus 5. Again, our m value needs to be the same. Our b value can be anything. So I'm just going to leave it y equals negative 3x. My b is 0 in that case. Again, as long as it's not positive 5, it doesn't matter what your b value is. So that's my answer there. Thank you for watching. And for more math tutorials, please subscribe to our channel, Friendly Math 101.