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

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