Symmetric Form of the Equation of a Line
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 a and the y-intercept b of this line represented in a Cartesian plane.
The symmetric form is presented like this: [latex]\dfrac{x}{a} + \dfrac{y}{b} =1[/latex], 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 [latex]\small{m = \dfrac{-b}{a}}[/latex] where [latex]m[/latex] represents the slope of the line. This result is obtained by isolating [latex]y[/latex] in the equation [latex]\small{\dfrac{x}{a} + \dfrac{y}{b} =1}[/latex] multiplying the two sides by [latex]b[/latex] to obtain the functional form of this equation: [latex]\small{y = \dfrac{–b}{a} x + b}[/latex], 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 ([latex]\frac{2}{3}[/latex], 0) and (0, 2), or a = 0.67 and b = 2.
Therefore, the equation of the line in its symmetric form is [latex]\dfrac{x}{0,67} + \dfrac{y}{2} = 1[/latex], or [latex]\dfrac{x}{(\frac{2}{3})} + \dfrac{y}{2} =1 [/latex].
The slope of this line is [latex]m = \dfrac{-2}{0,67}[/latex] or [latex]–3[/latex].
See also:
- Functional form of the equation of a line
- General form of the equation of a line