What is the Slope Formula

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Slope of a line, also known as ‘gradient of a line’ is the measure of steepness and direction of a line in the coordinate plane. Given any two points on the line, slope is the rate of change of ‘y-coordinates’ with respect to the ‘x-coordinates’. Slope is calculated by using the ‘rise-over-run’ method where we take the ratio of the rise with respect to the run. Slope is denoted by ‘m’ in general and it plays a very important role in writing equations of the lines.

Example 1:  What is the equation of the line passing through the points (1, 2) and (3, 4)?

Given two points: (1, 2) and (3, 4)
Slope of a line passing through any two points (x1, y1) and (x2, y2) is,
m = (y2 – y1)/ (x2 –x1)
This implies, (x1, y1) = (1, 2) and (x2, y2) = (3, 4).
This gives: Slope, m = (4 – 2)/ (3 – 1) = 2/2 = 1
Therefore, the slope of the given line is 1.

 
Example 2: What is the equation of the line passing through the points (4, -2) and (5, 1)?

Given two points: (4, -2) and (5, 1)
Slope of a line passing through any two points (x1, y1) and (x2, y2) is,
m = (y2 – y1)/ (x2 –x1)
This implies, (x1, y1) = (4, -2) and (x2, y2) = (5, 1).
This gives: Slope, m = (1 – (-2))/ (5 - 4) = (1 + 2)/1 = 3/1 = 3.

Therefore, the slope of the given line is 3.

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