Writing Linear Equations

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Linear equations are the equations in the standard form of Ax + By = C, where A, B and C are integers and ‘A’ and ‘B’ are not equal to 0. Linear equations consist of variables which have the highest exponent as ‘1’ and these equations can be solved to get the values of the variables. In a coordinate plane, given a point on the line and the slope of the line, we can write the equation of the line, which is always in the form of a linear equation.
 
Example 1: Write the equation of a line with a slope of 1 and passing through the point (2, 5).
Given: Slope of the line, m = 1
Point = (2, 5)
Point –slope form of a line==> (y – y1) = m(x – x1)
Therefore we get: (y – 5) = 1(x – 2)
This gives: y – 5 = x – 2
Simplifying the equation we get: x – 2 – y + 5 = 0 ==> x – y + 3 = 0

Hence the linear equation can be written as x – y = -3.
 

Example 2: Write the equation of a line with a slope of -2 and passing through the point (3, -4).
Given: Slope of the line, m = -2
Point = (3, -4)
Point –slope form of a line==> (y – y1) = m(x – x1)
Therefore we get: (y – (-4)) = -2(x – 3)
This gives: y + 4 = -2x + 6
Simplifying the equation we get: y + 4 + 2x – 6 = 0 ==> 2x + y - 2 = 0.

Hence the linear equation can be written as 2x + y = 2.

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