# Linear functions and equations

The general form of linear equations of two variables x and y is ax + by + c = 0, where a , b, c are any real numbers. The degrees of the variables x and y should be one. if the degrees of the variables x and y are other than one the its non-linear equations.

The graph of linear functions are straight lines on cartesian co-ordinates plane.  Consider a linear equation -2x + y  = 1 whose graph is given below.

1. Horizontal lines (y = b)

If the coefficient of x term is zero then linear equation can be expressed in the form y = constant. The graph of these functions are horizontal lines on the cartesian plane. The graph of the line y = b is a horizontal line, parallel to x axis and intersect y axis at (0,b).

Use the interactive graph given below to see the graphs of the liens of the form y = constant.

2. Vertical lines (x = a)

If the coefficient of  y term is zero in ax + by = 0, then linear equation can be expressed in the form y = constant. The graph of these functions are vertical lines on the cartesian plane. The graph of the line x = a is a horizontal line, perpendicular to x axis and intersect x axis at (a,0).

Use the interactive graph given below to see the graphs of the liens of the form x = constant.

3. Slant lines (y = mx + c)

Consider the linear equations in y = mx + c is called slope and intercept from, where m and c are real constants.

The graph of y = mx + c is a straight line with the slope or gradient of ‘m’ and the y axis intercept ‘c’.

Use the interactive graph given below to see the graph of y = mx + c.