What is the slope of the line that passes through the origin and the point two, five?
Okay, so I’ve drawn a little sketch here to help us visualize what’s happening. So we have a line and it’s passing through two points. It passes through the point two, five, but also the origin which actually the point zero, zero.
Okay and what we want to do is we want to find the slope of this line or how steep the line is. To calculate this, we have a formula to help us, which is that slope is equal to the change in 𝑦 over the change in 𝑥. Some people might have said the rise over the run or how much it moves up and down over how much it moves across. The more formal way of representing it is saying that 𝑚 — and 𝑚 is our slope — is equal to 𝑦 two minus 𝑦 one over 𝑥 two minus 𝑥 one, where these are actually the 𝑥- and 𝑦-coordinates of two points.
Okay, so let’s use this formula to help us find the slope of our line. So the first thing that we’ve actually done is label the coordinate points. We’ve got 𝑥 one, 𝑦 one 𝑥 two, 𝑦 two. And now because we have these and we know what they are, we can substitute them into our formula to help us find the slope.
So first of all, we have 𝑚 is equal to and then we have five minus zero. And that’s because that’s our 𝑦 two is five and our 𝑦 one is zero. And then, this is divided by two minus zero and this time because 𝑥 two is two and 𝑥 one is zero. So therefore, we can say that the slope of the line that passes through the origin and the point two, five is equal to five over two.