Slope - intercept form of the equation of a line

The equation of a line can be written in many forms. the simplest of these is the slope intercept form of the equation of a line.

This can be regarded as a template of writing an equation. The template of all equations written in this form is as follows:

y = mx + b

Template means that this is a symbolic equation. In this equation, 'm' and 'b' are representing the values of slope and y-intercept of a line. For example, in the equation y = 2x + 4, 'm' holds the value of 2 and 'b' holds the value of 4. Therefore, the slope of this equation is 2 and the y-intercept is 4.

Characteristics of the slope intercept form of the equation of a line:

• The variable 'y' is present isolated on the left hand side.
• The variable 'y' does not have any coefficients
• The variable 'x' and the constant term 'b' are present on the right hand side.
• The variable term 'mx' is written first, then the constant 'b' is written.

Converting any given equation into slope intercept form:

Any given equation of a line can be rewritten in the slope intercept form. You use simple algebra to convert an equation into the slope intercept form. While converting any given equation to the slope intercept form, you have to keep in mind the above mentioned characteristics of this form.

Let us take an example to see how to convert an equation to the slope intercept form:

Convert this equation into slope intercept form: 3y + 4x = 5

• First take 'x' to the other side of the equal to sign. To do this, subtract 4x from both sides. Now we get: 

3y = 5 - 4x

• Now write the term '-4x' first on the right hand side:

3y = -4x + 5

• Now we have to remove the coefficient of 'y'. So divide both sides by 3 in order to do so. Now we get:

y = (-4x + 5)/3

• Distribute the denomniator 3 amongst the numerators '-4x' and '5'. So we get:

y = -4x/3 + 5/3

Importance of the slope intercept form of the equation of a line:

This form of the equation of a line is very useful and an equation is mostly written in this form in order to get the slope and y-intercept of the line by just looking at the numbers at the positions of 'm' and 'b' respectively. Thus you are many times asked to write an equation in the slope-intercept form in maths.

How to get the slope and y-intercept of a line from the slope intercept form :

If the equation of a line is not written in the slope intercept form, you first have to convert it into the slope intercept form as described above. Then you can derive the slope and y-intercept of the line by the following steps:

• Compare the equation with the slope intercept form of the equation of a line y = mx + b.
• The number in place of 'm' will be the slope of the line.
• The number in place of 'b' will be the y-intercept of the line.
• The signs of the numbers in place of 'm' and 'b' are also taken into consideration.

For example, for the equation y = 3x - 4,

• The number in place of 'm' is 3. Therefore slope = 3.
• The number in place of 'b' is -4, therefore y-intercept = -4.