University:
College
Course:
College Mathematics
Academic year:

2023
Views:

132

Pages:

3
Author:

anon

Mathematics: Gradient of a Line Finding the gradient of a line: The gradient is a measure of “how steep” a line is. The word steepness is no stranger to most of you – the word most frequently appears during hikes. “The mountain is so steep, we might slide down!”. In this lesson, we’re going to learn how to calculate the steepness. Let’s say we have the cross-section of a mountain: That’s actually a line but for the moment, let’s assume otherwise. We want to calculate the steepness of the trail in the mountain (aka, the line), or the gradient. How do we do that? Well, the gradient is measure by the change in the y-coordinates in the slope divided by the x coordinates in the same slope. If we were to write this in user-friendly terms, we would arrive at something like this: We represent the gradient using the symbol “m”. But in reality, you can use any alphabet you like. a,g,d,g, whatever floats your boat. So, you may be asking, there’s only a line, no coordinates! Well, look below! Here’s another line in a Cartesian Coordinate Plane (if you have no idea what I’m talking about, review previous lesson). To calculate the gradient, simply find the change in y-coordinates by the change in x-coordinates, or the formula shown above. Let’s do an example. 1) A slope is 500 m high from the ground, and 400 m long. Find the gradient. To make ourselves comfortable, we’ll position our slope starting from the origin, coordinates (0,0). The coordinates of the end of the slope is when the height is 500 m and the length is 400 m. As height is modeled by the y-axis and length by the x-axis, the coordinates for which we can call the other endpoint of the slope will be (400,500). Therefore: The gradient, given by the formula, will then be: Negative and Positive Gradients Sometimes, you might be asked to identify whether the line segment has a negative or positive gradient without making any calculations