# Straight Lines, General Equation of First Degree, Conversion of General Equation of a Line into Various, Conversion into Slope – Intercept Form, Conversion into Intercept Form

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## General Equation of First Degree

You know that a linear equation in two variables and is given by

In order to understand its graphical representation, we need to take the following three cases.

Case-1: (When both and are equal to zero)

In this case is automaticaly zero and the equation does not exist.

Case-2: (When and )

In this case the equation (1) becomes. or and is satisfied by all points lying on a line which is parallel to x-axis and the y-coordinate of every point on the line is . Hence this is the equation of a straight line.

The case where and can be treated similarly.

Case-3: (When and )

We can solve the equation (1) for and obtain.,

Clearly, this represents a straight line with slope and y – intercept equal to .

## Conversion of General Equation of a Line into Various

If we are given the general equation of a line, in the form , we will see how this can be converted into various forms studied before.

## Conversion into Slope – Intercept Form

We are given a first degree equation in and as

Are you able to find slope and y-intercept?

Yes, indeed, if we are able to put the general equation in slope-intercept form. For this purpose, let us re-arrange the given equation as.

as,

Or (Provided)

Which is the required form. Hence, the slope , intercept .

Example:

Reduce the equation to the slope – intercept form. Here find its slope and intercept.

Solution:

The given equation is,

Or

Or

Here slope and interecept

## Conversion into Intercept Form

Suppose the given first degree equation in and is

In order to convert (1) in intercept form, were arrange it as or or (Provided and )

Which is the required converted form. It may be noted that intercept on x – axis and intercept on y – axis

Example:

Reduce into the intercept form and find its intercepts on the axes.

Solution:

The given equation is,

Or or,

The x– intercept and, y – intercept