The gradient of a line, also known as its slope, is a measure of its steepness. It describes the ratio of the vertical change to the horizontal change between any two points on the line. consider the diagram below:
Line A is closer to the vertical axis but farthest from the horizontal axis. Line A is said to be steepest among the lines A, B, C, D because it is the closest to the vertical line. The steepness of a line is it’s gradient.
consider yourself traversing through the lines horizontally via line Q and vertically via P.
You will arrive at A first while travelling horizontally but while moving vertically you will arrive at D first. D is closer to horizontal position but far from vertical position. The lines illustrated above are moving in two dimensions: Horizontal and vertical dimensions.
consider yourself moving along line B; you will realize that, you have changed horizontal and vertical distance in the movement.
As you move along B, you will have covered distance PY vertically and distance QY horizontally. The ratio of vertical distance covered to the horizontal distance covered gives the gradient(steepness of a line).
If vertical distance covered is larger than the horizontal distance, the line is said to have a steep gradient.
We can get gradient of a line by finding vertical and horizontal change from any two arbitrary points on a line.
Let us take any two points on a Cartesian plane shown above, x1 corresponds to y1 and x2 corresponds to y2.
the horizontal distance covered between P and Q = x1 -x2
the vertical distance covered between P and Q = y1 – y2
Gradient will thus be given by:
Leave a Reply