Writing Linear Equations

Writing Linear Equations 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.