Lesson video

Hello, my name is Mr. Clasper.

And today we are going to be finding intercepts and gradients from a line given in any form.

Here's the general equation of a straight line.

We often write lines like this as the value of M will give us the gradient, and the value of C will give us the Y-intercept.

So in an equation written in this form, the coefficient of X will give us the gradient and the constant will give us the Y-intercept.

The straight line Y equals seven X minus nine has a gradient of seven.

This is because the coefficient of X is seven and intercepts the Y axis at zero negative nine.

This is because our constant is negative nine.

Here are some questions for you to try.

Pause the video to complete your task and click Resume once you're finished.

And here are your solutions.

So remember for question one, you only need to identify the gradient, which is given by the coefficient of X.

And for question two, we only need the Y-intercept.

If you've given these as coordinates, that will be fine.

So if a part A, if you've written down zero three, this is fine.

For B zero, negative two.

For C zero, zero, and for D, zero, six.

Here is another question for you to try.

Pause the video, to complete your task and click Resume once you're finished.

And here are your solutions.

So for this question, we needed to identify both the gradient and the Y-intercept or the M component of the general equation, and the C component of this equation.

Let's take a look at this example.

Find the gradient at intercept of Y minus five X is equal to nine.

This is a straight line.

However, at the moment, it is not written in the form of Y equals MX plus C.

If we can write it in the form of Y equals MX plus C, we can easily identify our gradient and our Y intercept.

Let's rearrange this equation.

So if we add five X to both sides of the equation, we would get Y equals five X plus nine.

And this means we have the gradient of five and a Y-intercept of nine.

Let's try this example.

We have the equation two Y plus six X is equal to 10.

Again, we need to write this in the form of Y equals MX plus C, to identify our gradient and our intercept.

So if we subtract six X from both sides, we would then get two Y is equal to negative six X plus 10.

And then to make Y the subject, we need to divide both sides of my equation by two.

So this means Y is equal to negative three X plus five.

And therefore my gradient is negative three, and my Y-intercept is five.

Here is your last question.

Pause the video to complete your task and click Resume once you're finished.

And here we are your final solutions.

So remember, for these equations, we must rearrange to make each equation in the form of Y equals MX plus C.

And once you've got Y as the subject, you should be able to easily identify your gradients and your intercepts.

And that brings us to the end of our lesson.

So we've been finding intercepts and gradients from a line written in any form.

Why not give the exit quiz a go to show off your new skills? I'll hopefully see you soon.