Video: Find the 𝑥-Intercept of a Straight Line

The 𝑥-intercept of a straight line is the point at which the graph of the line cuts the 𝑥-axis. We look at how to substitute a 𝑦-value of zero into the line’s equation to evaluate the corresponding 𝑥-coordinate and hence calculate the 𝑥-intercept.


Video Transcript

Find the 𝑥-intercept of a straight line. Now the 𝑥-intercept of a straight line is where it crosses the 𝑥-axis. So for example- so for example, with this graph we can see the line crosses the 𝑥-axis here. And the important thing about this is not only that it crosses the 𝑥-axis, but that is also you’ll notice where 𝑦 is equal to zero.

And this is the fact that we’re going to use to help us find 𝑥-intercept given a linear equation. So looking at our first example, we’re asked to find the 𝑥-intercept of the equation 𝑦 equals three 𝑥 plus six. Well remember that when we’re finding the 𝑥-intercept, then that means that 𝑦 is equal to zero. So substituting zero in for 𝑦, we will get zero is equal to three 𝑥 plus six. And now to find the value of 𝑥 or the 𝑥-intercept, we’d simply just have to solve for 𝑥. So subtracting six from both sides, we’ll get negative six on the left-hand side is equal to three 𝑥 on the right-hand side. And this is three multiplied by 𝑥. So to get rid of the times by, we must divide by. So dividing both sides by three, well negative six divided by three is negative two and that is of course equal to 𝑥. So our 𝑥-intercept is negative two. And we could say the coordinate where our line 𝑦 equals three 𝑥 plus six crosses the 𝑥-axis is negative two, zero.

Let’s look at one more example. Find the 𝑥-intercept of five 𝑥 plus two 𝑦 minus twenty equals zero. We have to remember to find the 𝑥-intercept, we must set 𝑦 equal to zero. So first of all, let’s write the equation back out. But this time where we see 𝑦, which is after two, we’ll put zero. So we have five 𝑥 plus two multiplied by zero minus twenty equal zero. Now two multiplied by zero is zero. So we’ve got five 𝑥 add zero, so just five 𝑥 minus twenty.

And now we have a simple two-step equation: first to solve for the value of 𝑥. So we can see that we’ll have to add twenty to both sides. And then on the left-hand side, we have five 𝑥 and that will be equal to zero add twenty, which is twenty. And then that’s five multiplied by 𝑥 is equal to twenty. So the opposite of times by is divide by. Dividing both sides by five, we get that 𝑥 is equal to four. And again if we were asked for the coordinate of the intercept, we would simply write four, zero. There we have it. So to find the 𝑥-intercept of any line, we must simply substitute in the value of 𝑦 is equal to zero.

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