What is the Slope Formula

What is the Slope Formula 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.