Forms of Linear Functions

A polynomial functions of single degree is defined as a linear functions. It relates a dependent variable with an independent variable in a simple way. Mathematical equation in which there is no independent-variable is raised to a power greater than one. A simple linear function with one independent variable (y=a+bx) traces a straight line when plotted on a graph. It is also called as linear equation.

The function is defined by f the first degree equation: f = { ( X, Y)/ Y = mX + b } where m and b are constants, x and y is called a linear functions. The function derives a straight line while graphing.

Functions such as these gives graph that are straight lines, and, thus, the name linear. There are three main forms in linear functions. They are as follows,

Slope-Intercept Form is given by y = mx +b.
Point Slope Form is given by m = (y - y1) / ( x – x1).
General Form is given by Ax + By + C = 0.


Steps to Solve Linear Functions

Solving the given function by altering its position and simplifying the equation to get Y is generally known as solving linear equations. The solutions of these equations provide solutions of the corresponding practical problems. The important steps in the solution of these word problems are listed below:

Read the problem carefully and note down (i) what is given, and (ii) what is required.
Denote the unknown quantity by a literal x, y, z, u, v, w etc.
Translate the statements of the problem step by step into mathematical statements, to the extent possible.
Look for the quantities that are equal. Write the equations corresponding to these equality relations.
Solve the equations written in Step 4 above.
Check the solution by substituting the value of the unknown found in Step 5 above into the statements of the problem.


Solved Examples

Example: Solve for x and y, where, y = x+ 13 and 2x - y - 10 = 0

Sol : plug y = x + 13 in 2x - y - 10 = 0

=> 2x -(x + 13) - 10 = 0

=> x - 23 = 0

=> x = 23

Algebra is widely used in day to day activities watch out for my forthcoming posts on Fractions and Equivalent Decimals and wb primary. I am sure they will be helpful.

now, plug x = 23 in 2x - y - 10 = 0

=> 46 - y - 10 = 0

=> - y + 36 = 0

=> - y = - 36

=> y = 36