# Write an Equation of the line

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In a coordinate plane, by joining few points we can draw a straight line. The equation of this straight line formed can be written by taking any two points on the line and writing the equation in either slope-intercept form or point-slope form of the line. Slope of a line is the direction or the steepness of a line and it is useful while writing the equation of a line. Equation of a line is written in terms of the variables ‘x’, ‘y’ and also a constant.

Example 1: Write the equation of a line with a slope of 3 and passing through the point (1, 2).
Given: Slope of the line, m = 3
Point = (1, 2)
Point –slope form of a line==> (y – y1) = m(x – x1)
Therefore we get: (y – 2) = 3(x – 1)
This gives: y – 2 = 3x – 3.
Simplifying the equation we get: 3x – 3 – y + 2 = 0 ==> 3x – y – 1 = 0
Hence the equation of the given line is 3x – y – 1 = 0

Example 2: Write the equation of a line with a slope of -1 and passing through the point (4, 3).
Given: Slope of the line, m = -1
Point = (4, 3)
Point –slope form of a line==> (y – y1) = m(x – x1)
Therefore we get: (y – 3) = -1(x – 4)
This gives: y – 3 = -x + 4
Simplifying the equation we get: y – 3 + x – 4 = 0 ==> x + y - 7 = 0
Hence the equation of the given line is x + y – 7 = 0.