# Video: Find the π¦-Intercept of a Straight Line

Learn how to rearrange linear equations into the π¦ = ππ₯ + π or π¦ = ππ₯ + π general format in order to identify the π¦-coordinate of the point at which the line crosses the π¦-axis (when the π₯-coordinate is zero).

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### Video Transcript

Find the π¦-Intercept of a Straight Line

Now for every straight line, the general form is π¦ equals ππ₯ plus π, where π is the slope of the line, but we wonβt worry about that this video, and π is the π¦-intercept.

The π¦-intercept is where the line crosses the π¦-axis or intercepts the π¦-axis. So for example, given this line, we can see that it crosses the π¦-axis here. Now the other important thing about this is that π₯ is equal to zero.

And we can either use the general form as we have here or the fact that π₯ equals zero at the π¦-intercept to help us find the value of it. In some cases, for this one for example, itβs quite easy to see which is the more simple way to find it. So, if we have to find the π¦-intercept of the line π¦ equals four π₯ 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 weβve got π¦ equals ππ₯ plus π. And for this one, we can see π¦ equals four π₯ plus seven. So the π¦-intercept is seven and we could say if weβre asked for the coordinate, zero, seven.

Now letβ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 π₯ equal to zero because we would simply say π¦ equals four multiplied by zero plus seven. Well, four multiplied by zero is just zero, so weβre left with π¦ equals seven, gives us exactly the same answer either way.

Now if we are asked to find the π¦-intercept of two π¦ plus four π₯ equals fifteen. Again weβ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 π₯ equals zero.

So if we chose option number one, we would need to rearrange to get just π¦ equals some π₯ plus π. So, first off, we would need to subtract four π₯ from both sides, giving us two π¦ equals negative four π₯ plus fifteen. And then, as that is, two multiplied by π¦, the opposite of times by is divide by, so weβd have to divide, be careful, every single term by two.

We must be careful on this fact that itβs every single term because sometimes we forget and we miss the term, so itβs important to remember every single one. Well that gives us anyway π¦ on the left-hand side, and thatβs equal to negative two π₯ plus fifteen over two or we could say seven point five.

So this tells us that the π¦-intercept is seven point five. Now our other option was to substitute in π₯ equals zero. So first of all, we would have two π¦ equals four multiplied by zero equals fifteen.

Well we know four multiplied by zero is just zero, so we have two π¦ equals fifteen. And as itβs two multiplied by π¦, the opposite of times by is divide by, so weβll get that π¦ 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 π¦ equals ππ₯ plus π, as in some cases weβll need to then use the general form later on for slopes and things like that. But if itβs a stand-alone question, thereβs no harm in just substituting in π₯ equals zero.