The symmetric form of the equation of a line is an equation that presents the two variables

*x*and*y*in relationship to the x-intercept**and the y-intercept***a***of this line represented in a Cartesian plane.***b*The symmetric form is presented like this: \(\dfrac{x}{a} + \dfrac{y}{b} =1\), where *a* and *b* are non-zero.

It should be noted that the symmetric form of the equation of a line does not make it possible to find the slope of a line. To do that, you must use the relationship \(\small{m = \dfrac{-b}{a}}\) where \(m\) represents the slope of the line. This result is obtained by isolating \(y\) in the equation \(\small{\dfrac{x}{a} + \dfrac{y}{b} =1}\) multiplying the two sides by \(b\) to obtain the functional form of this equation: \(\small{y = \dfrac{–b}{a} x + b}\), in which the coefficient of

*x*is the slope of the line.### Example

In this illustration, we can see that the coordinates at the origin of the line are (\(\frac{2}{3}\), 0) and (0, 2), or a = 0.67 and b = 2.

Therefore, the equation of the line in its symmetric form is \(\dfrac{x}{0,67} + \dfrac{y}{2} = 1\), or \(\dfrac{x}{(\frac{2}{3})} + \dfrac{y}{2} =1 \).

The slope of this line is \(m = \dfrac{-2}{0,67}\) or \(–3\).

### See also:

- Functional form of the equation of a line
- General form of the equation of a line