Straight Line (H)

But what if the information you are given isn’t so straightforward? What if you know the gradient and the coordinates of a point it passes through, but this point isn’t on the y-axis? A good understanding of the link between the algebra and the geometry will help you solve these types of problems.

Let the coordinates of the point it passes through be (x₁, y₁). Substitute these, along with the gradient, into the general equation y - y₁ = m(x - x₁). Multiply out the brackets and tidy up.

You may be given even less information, such as only being told two points it passes through. In this case you firstly need to calculate the gradient (change in y over change in x), then use the previous technique with one of the points.

Equations may be given in the format ax + by = c. This is useful if you want to find both the x- and y-intercepts, but you will need to rearrange it to identify the gradient.