Lesson video

Hello, my name is Ms Parnham.

And in this lesson, we're going to find the equation of a straight line passing through two given points.

Here we have two coordinates on a grid.

We have 2,2 and 4,1 and we want to find the equation of the straight line passing through them.

So if we first look at the vertical change on horizontal change, we have a vertical change of negative 1, a horizontal change of 2.

So the gradient is negative 1 over 2 or negative a half.

So we know that our equation starts with Y equals negative a half X.

And if we actually draw the line in, we can see we have an intercept of positive 3.

So Y equals negative a half X add 3.

Is there another way that we could have done that? Say for example, we didn't have the coordinate grid.

Well, let's start with Y equals negative half X plus C and use one of the coordinates that we know it goes through and let's use B.

So for 4,1 definitely lies on this line.

So 4 is the X coordinate.

So we'll replace X in our equation with 4 and 1 is the Y coordinate.

So we'll substitute Y with 1 and 1 equals negative a half multiplied by 4 plus C.

Well, negative a half multiplied by 4 gives us negative 2 and 1 equals negative 2 plus C.

So we add 3 onto negative 2 to make 1.

So this is another way of showing that our equation is Y equals negative a half X, add 3.

Here's a question for you to try, pause the video, to complete the task, and then restart the video when you're finished.

Here are the answers, the line between A and B has a gradient of 0.

5, or if you prefer a half and it has a Y intercept at 3.

So the two possible ways to write the answer are Y equals 0.

5 X plus 3, or Y equals a half X plus 3.

We're going to work out the equation of the straight line that passes through -2,3 and 0,1.

So we can plot those on our coordinate grid and draw a line through them.

Let's work out the gradient.

We have a horizontal change of 2 and a vertical change of negative 2.

So negative 2 divided by 2 is negative 1 for our gradient.

So we know that the equation will start with Y equals negative X, let's just work out the constant.

From our graph, we can see that this line intercepts the Y axis at positive 1.

So C equals 1, and therefore our final equation is Y equals negative X add 1.

Let's find the equation of a straight line passing through two coordinates without the use of an accurate coordinate grid.

We can draw a sketch to show the two points that we're talking about and join them with a line segment, but we can work out the gradient from the coordinates because this is vertical change divided by horizontal change.

So if we subtract negative 12 from 1, this will give us 13 for the horizontal change and then subtracting negative 15 from 24 gives us 39.

We must ensure that when we subtract, we have done in this instance, the second coordinate subtracts the first coordinate we need to do the same for both X and Y so that we get the science correct.

And the gradient is 39 divided by 13, which is 3.

And that has come from 24 subtract negative 15 over 1 subtract negative 12.

So we know the equation of our line will start with Y equals 3 X.

We just need to work out C.

And to do that, we will pick either one of these coordinates.

Now you will probably want to pick the one that involves positive values and that's fine.

So we know that Y is 24, when X is 1.

So 24 equals 3 multiplied by 1 plus C.

Well, that means that 25 is 3 plus C.

So C must be 21.

So our final equation is Y equals 3 X add 21, Here are some questions for you to try pause the video, to complete the task, and then restart the video when you're finished.

Here are the answers.

In question three, we first have to find the equation of the line passing through 10,2 and 5,12.

So we have a vertical change of 10 and a horizontal change of negative 5.

So 10 divided by negative 5 gives us a gradient of negative 2.

So we know that we're starting with Y equals negative 2 X.

So if we use the coordinate 10,2 we substitute X equals 10 into this.

So that would give us initially negative 20.

And that means we need to add 22 to get the Y coordinate of 2.

So we have the equation of Y equals negative 2 X plus 22.

Now 7,9 will lie on that line if, when we substitute 7 for X, we get 9 for Y.

So substituting 7 gives us Y equals negative 14 plus 22.

And this equals 8.

So 7,9 is not on the line.

That's all for this lesson.

Thank you for watching.