[tex]ax + by + c = 0 \\ \\ ax + by = - c [/tex]
Divide both side by -c
[tex] \frac{ax}{ - c} + \frac{by}{ - c} = \frac{ - c}{ - c} \\ \\ \frac{x}{ \frac{ - c}{a} } + \frac{y}{ \frac{ - c}{b} } = 1[/tex]
Equation of line in Intercept form :
[tex] \frac{x}{a} + \frac{y}{b} = 1 \\ [/tex]
[tex]x \: intercept \: : a = \frac{ - c}{a} \\ \\ y \: intercept \: : b = \frac{ - c}{b} [/tex]
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Answers & Comments
Given :
[tex] = \frac{1}{8 + 6 \sqrt{2} } \\ [/tex]
To do :
Solution Explanation :
[tex]= \frac{1}{8 + 6 \sqrt{2} } \times \frac{8 - 6 \sqrt{2} }{8 - 6 \sqrt{2} } \\ \\ = \frac{8 - 6 \sqrt{2} }{(8) {}^{2} - (6 \sqrt{2}) {}^{2} } \\ \\ = \frac{8 - 6 \sqrt{2} }{64 - 72} \\ \\ = \frac{8 - 6 \sqrt{2} }{ - 8}[/tex]
[tex]ax + by + c = 0 \\ \\ ax + by = - c [/tex]
Divide both side by -c
[tex] \frac{ax}{ - c} + \frac{by}{ - c} = \frac{ - c}{ - c} \\ \\ \frac{x}{ \frac{ - c}{a} } + \frac{y}{ \frac{ - c}{b} } = 1[/tex]
Equation of line in Intercept form :
[tex] \frac{x}{a} + \frac{y}{b} = 1 \\ [/tex]
[tex]x \: intercept \: : a = \frac{ - c}{a} \\ \\ y \: intercept \: : b = \frac{ - c}{b} [/tex]