Gradient Of A Straight Line

What is a gradient of a line?


Every straight line that is drawn on a graph is either horizontal (side to side), vertical (up and down) or has a slope.

The gradient of any line is a measure of the steepness of that slope and is an important part of both drawing and interpreting lines.

When we talk about the slope of a line, we are looking at the direction of the line from left to right and we can calculate the slope of the line by first choosing any two points on the line.

We can then create a right-angled triangle with the line as the hypotenuse.


How is a gradient calculated?


The gradient of the line is calculated as

or distance up over distance across between the two points.

We can then create a right-angled triangle with the line as the hypotenuse.


An Example


In our example, we have a straight line on a graph and we chose two points on the line.

Let’s choose the points A(2, 3) and B(4, 7).

We then draw a right-angled triangle by creating two lines, a horizontal line and a vertical line.

If we measure the horizontal line the length is two (2), and if we measure the vertical line the length is four (4).

Using our calculation above, that is GRADIENT = RISE OVER RUN, we get the gradient of the line is 4/2 which is 2.

Therefore, the gradient of this line is two.

An Example



We now have a line that is sloping down from left to right and because of that we expect our gradient to be a negative number.

Measuring the lengths, the horizontal from left to right is 2 in length, but the vertical actually does not go up, it goes down, so it -6.

-6/2 is -3, and that’s the gradient of this line.

Some suggestions when drawing your lines to complete the right-angled triangle are

  • Choose two points that are reasonably far away from each other, this makes for better accuracy in your calculations, especially when dealing with real life graphs.
  • Try choosing points that you are confident of the values. In other words, choose points that possibly are at major cross points and easily identified.
  • If you are using a grid scale on the graph, be aware of what values the graph blocks have, as some graphs have different scales to others.