The slope is the steepness and direction of a line. In mathematical expression, the slope of a given line is expressed as the ratio of the vertical change, or rise, to the horizontal change, or run, between any two points of that given line. There is an expression stating the slope, most commonly called the formula for slope. 

Formula

The formula for slope is given as,

Where,    are the coordinates of two distinct points on the line.

Solved Problems

Problem 1: Find the slope of a line whose coordinates are (2,7) and (8,1)?

Solution:

m = (1 − 7/ 8 − 2)

m  = −6/6

m = − 1

Problem 2: If a line passes through the points (4, b) and (2, -9) with slope 3, then what is the value of b?

Solution:

Given,

3 = (-9 – b)/(2 – 4)

3 = (-9 – b)/(-2)

-9 – b = 3(-2)

-9 – b = -6

b = -9 + 6 = -3

Therefore, the value of b is -3.

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