Linear Functions

Linear Functions An algebraic expression with degree 1 is called as a linear expression. The standard form of a line is Ax + By = C.Here A, B and C are constantsx and y are variablesSo Ax+ By = c is a linear equation with two variables.Linear Equations can be represented in many forms. A linear equation may have any number of variables. Suppose it is n then the linear equation is of the form a1x1 + a2x2+a3x3++an xn = CC C is a constant and x1, x2.,xnare variables 1)What is the degree of x + 3y = 12 ? The power of x is 2 and the power of y is 1. Degree = Highest power = 2 Example 1: 2x + 3 = 19 (Linear equation in one variable) 2x +3- 3 = 19 3 (Add -3 on both sides) 2x/2 = 16/2(Divide by 2 on both sides) x = 8 Example 2: 4x + 3y + 7 = 0 (Linear equations in two variables x y) NOTE: Number of solutions of an equation is equal to the degree of the equation. 4) Choose a Linear expression from the following (a) y (b) 6x/2y (c) 2xy + 6 (d) 7x + 9y (e) y Answer: d 5) x + 2 = 12. Solve for x x + 4 = 12 (Square the number) x + 4 4= 124 (Add -4 on both sides) x = 8