Lesson video

Hello, my name is Miss Parnham.

And in this lesson, we're going to learn how to write the equation of a straight line, if parallel to a line and passing through any point.

We're going to find the equation of a line parallel to y equals five x subtract seven that passes through the point three 28.

So if it is parallel to y equals five x subtract seven, then it has the same gradient, which is the x coefficient of five.

So we know our line starts with y equals five x, but now we need to work out the c.

So if we look at this coordinate, we've got three 28.

So is c 28? No it's not.

c would only be 28, if we were talking about the coordinate zero 28, so when x was zero, and therefore five x was also zero, so we're going to start in exactly the same way in this example.

And the gradient is indeed the same.

So our equation does start with y equals five x plus c.

And now we need to work out that c.

We know that three 28 lies on the line.

So we're going to substitute the x value of three into this equation.

So y equals five times three, add something, while we know that five times three is 15.

And if y is 28, then c must be 13.

So we know that the equation is y equals five x plus 13.

Now we're going to look for a line which is parallel to y equals a half x plus three and it passes through the point eight negative five So we start in exactly the same way, by identifying the gradient of the line.

If it's parallel, our line has the same gradient, and that is the x coefficient of a half.

So we know that our line starts with y equals a half x, we just need to calculate what c is.

So let's substitute the point that we've been given that we know that it passes through.

Let's substitute the value for x which is eight and put that in an equation which is equal to negative five.

So negative five equals a half multiplied by eight plus c.

Well, a half multiplied by eight is four.

So negative five equals four, add c.

So if we add in something onto four and getting negative five, then it is a negative value or adding on and it is in fact, negative nine.

So the equation of our line is y equals a half x subtract nine.

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 part C and D, we are substituting negative values.

So in part C, multiplying our value for the x coordinate of negative two by negative two produces four, so we have to subtract four to get that y coordinate of zero.

In D, we're multiplying negative three by the x coordinate of negative 10.

And that produces 30.

So we need to subtract 32 to get the y coordinate of negative two.

Now in part we are multiplying 12 by negative one quarter and this equals negative three, and then we need to add one to get the y coordinate of negative two.

We're looking for a line now, which is parallel to x plus two y equals 12 and passes through the point four 31.

The line we have been given is not in the form y equals mx plus C.

So it's not immediately obvious what the gradient is, because our line that we're looking for has the same gradient as this.

So let's rearrange that now.

So if we're going to isolate y, we need to subtract x from both sides.

That gives us two y equals negative x plus 12.

And then dividing through by two gives us y equals negative a half x plus six.

So the equation of our line because it shares same gradient of negative a half is going to start with y equals negative a half x, we just need to work out what the constant value is.

And we're going to use the coordinate four 31.

So we know that there's lies on the line.

So when x is four, this will produce an answer for y of 31.

So if we put that into our equation 31 equals negative a half multiplied by four plus C.

Well, negative a half multiplied by four is negative two.

So 31 equals negative two plus C.

Well, we need to add 33 on to negative two to get 31.

So our final answer for the equation of the line is y equals negative a half x plus 33.

Here's 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.

If you also want to check that your rearrange correctly into y equals mx plus c form, then you should have got y equals two x plus three for part A, in part B y equals x, subtract two.

In part C, y equals three halves x, subtract two, indeed y equals two x subtract three halves and then in part y equals negative a half x subtract two and where I've said three halves that you could have written 1.

5, or one and a half, and instead of negative a half, you could have written negative nought point five or totally acceptable.

That's all for this lesson.

Thank you for watching.