This week in Math 10, I have chosen to talk about the forms of linear equations.

Linear equations are another term for a relation that forms a straight line. You can read my post on X and Y intercepts to learn more about relations. There are three forms to linear equations with different uses.

• General form
• Slope y-intercept form (AKA: slope-intercept, slope-y)
• Point-slope form

Starting with general form, it is the most simple form of a linear equation. The problem is, it lacks all useful information, but can be used to determine X and Y intercepts, as shown in the earlier blog post. It is written in the form where M is the slope of the equation.

General form can be easily converted to slope y-intercept form by subtracting the Y and its coefficient from both sides of the equation (like when solving equations.) Note that if the coefficient was negative, it would be added instead.

Dividing everything by we convert to slope y-intercept form.

Slope y-intercept form is called as such because it contains the slope and y coordinate of the y-intercept of the line (the letter b representing the y-intercept coordinate.)

It is impossible to convert from either of the above forms to point-slope form, but point-slope form can be converted to slope y-intercept form, then to general form. It is written with the slope of the line and a single point.

where A and B represent the X and Y coordinates respectively of the point used in the equation.

To convert to slope y-intercept form, M is distributed to and B is moved to the X side the same equation solving method.