How to Calculate Gradient of a straight line joining 2 points

To calculate the gradient of a line two points $(x_1,y_1)$ and $(x_2,y_2)$ are needed. For example, Suppose we are given 2 points (2,4) and (5,10). The first coordinate is the x - coordinate and the second coordinate is the y-coordinate. If one of the points is denoted $(x_1,y_1)$ then the second point is denoted $(x_2,y_2)$ as shown below.

The Gradient Formula

The second step is to apply the gradient formula. The formula for gradient is \begin{align} m&= \frac{y_2-y_1}{x_2-x_1} \text { where m is the gradient} \end{align}
Let us now apply substitution where $x_1=2$ and $y_1 =4$ ; $x_2=5$ and $y_2=10$ \begin{align} m &= \frac{y_2-y_1}{x_2-x_1} \\ &=\frac{10-4}{5-2} \\ &=\frac{6}{3} \\ &= 2 \end{align} Thus our gradient is 2.

Marked Exercise

Question: Calculate the gradient of the line joining the following points. Enter your solution in the corresponding answer boxes. After answering click mark my work button.
(3,8) and (7,16)

(1,8) and (3,18)


Calculating Gradient Practice

If you would like to practice and gain more experience on calculating the gradient given 2 points, then you can visit the Gradient Quiz Generator . You will have plenty of revision and fun. There will be infinite number of questions. Detailed solutions for incorrect response are provided. Go to the gradient quiz generator now and start revising. If you would like to verify your homework or assignment then you can visit the Gradient Calculator here . The gradient calculator provides detailed solution for gradient when 2 coordinates are entered. It can be used as a home work helper.

Other Coordinate Geometry Tutorials

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  2. Finding the midpoint of a straight line given 2 points tutorial
  3. Finding the distance between 2 points tutorial