Find the 𝑦-Intercept of a Straight Line
Now for every straight line, the general form is 𝑦 equals 𝑚𝑥 plus 𝑐, where 𝑚 is the slope of the line, but we won’t worry about that this video, and 𝑐 is the 𝑦-intercept.
The 𝑦-intercept is where the line crosses the 𝑦-axis or intercepts the 𝑦-axis. So for example, given this line, we can see that it crosses the 𝑦-axis here. Now the other important thing about this is that 𝑥 is equal to zero.
And we can either use the general form as we have here or the fact that 𝑥 equals zero at the 𝑦-intercept to help us find the value of it. In some cases, for this one for example, it’s quite easy to see which is the more simple way to find it. So, if we have to find the 𝑦-intercept of the line 𝑦 equals four 𝑥 plus seven, you can see it would just be seven.
As this equation follows the general form for any linear equation, so we can see in the general form we’ve got 𝑦 equals 𝑚𝑥 plus 𝑐. And for this one, we can see 𝑦 equals four 𝑥 plus seven. So the 𝑦-intercept is seven and we could say if we’re asked for the coordinate, zero, seven.
Now let’s look at an example where we could use either method. We could also see with this example that it would work to substitute in 𝑥 equal to zero because we would simply say 𝑦 equals four multiplied by zero plus seven. Well, four multiplied by zero is just zero, so we’re left with 𝑦 equals seven, gives us exactly the same answer either way.
Now if we are asked to find the 𝑦-intercept of two 𝑦 plus four 𝑥 equals fifteen. Again we’ve got two options: option number one would to be rearrange the equation to the general form and option number two would be to substitute in 𝑥 equals zero.
So if we chose option number one, we would need to rearrange to get just 𝑦 equals some 𝑥 plus 𝑐. So, first off, we would need to subtract four 𝑥 from both sides, giving us two 𝑦 equals negative four 𝑥 plus fifteen. And then, as that is, two multiplied by 𝑦, the opposite of times by is divide by, so we’d have to divide, be careful, every single term by two.
We must be careful on this fact that it’s every single term because sometimes we forget and we miss the term, so it’s important to remember every single one. Well that gives us anyway 𝑦 on the left-hand side, and that’s equal to negative two 𝑥 plus fifteen over two or we could say seven point five.
So this tells us that the 𝑦-intercept is seven point five. Now our other option was to substitute in 𝑥 equals zero. So first of all, we would have two 𝑦 equals four multiplied by zero equals fifteen.
Well we know four multiplied by zero is just zero, so we have two 𝑦 equals fifteen. And as it’s two multiplied by 𝑦, the opposite of times by is divide by, so we’ll get that 𝑦 is equal to seven point five.
And we get exactly the same answer either way, so we could use either, but I would say is the most helpful usually is to rearrange into the form 𝑦 equals 𝑚𝑥 plus 𝑐, as in some cases we’ll need to then use the general form later on for slopes and things like that. But if it’s a stand-alone question, there’s no harm in just substituting in 𝑥 equals zero.