It gets annoying to draw a graph every time to find out the slope of a line as it requires you to draw an accurate graph and then calculate the slope of the line. However, it can be avoided by using the “Slope Formula” which is the general formula used to find out the slope of the line.
The Slope Formula is given by:
Slope = Change in x / Change in y
=> Slope = y2 – y1 / x2 – x1
To calculate the slope of any given line, you will need only two points from that line, (x1, y1) and (x2, y2).
Let us take an example to clarify how Slope Formula works!
Let us take two points on a line (16, 8) and (13, 7) on a straight line. To find the slope of the line, let us take any of these points to be (x1, y1) and the other one to be (x2, y2).
It doesn’t matter which point you choose because at the end the result will be the same. So, we choose (16, 8) to be (x1, y1) and the (13, 7) to be (x2, y2).
Now putting values in the formula;
Slope = (8 – 7) / (16-13) = 1/3
As mentioned earlier, it doesn’t matter which point you choose as (x1, y1) or (x2, y2) as the result will be the same!
Now, taking (13, 7) to be (x1, y1) and the (16, 8) to be (x2, y2)
Slope = (7 – 8) / (13 – 16) = -1/-3 = 1/3
Hence, the Slope will be the same no matter which point you chooose to be (x1, y1) or (x2, y2)!
Most of the times you will not be given the two points and you will have to identify those points from the graph.