Respuesta :
The equation of perpendicular line is [tex]$y=-\frac{11}{6} x+\frac{43}{6}[/tex].
What is the equation of a Straight Line ?
The equation of the straight line is represented by
y = mx + c
where m is the slope , and c is the intercept on y axis.
Calculate the slope m of BC using the slope formula
[tex]$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$[/tex]
with [tex]$\left(\mathrm{x}_{1}, \mathrm{y}_{1}\right)=\mathrm{B}(8,4)$[/tex] and [tex]$\left(\mathrm{x}_{2}, \mathrm{y}_{2}\right)=\mathrm{C}(-3,-2)$[/tex]
[tex]$m_{B C}=\frac{-2-4}{-3-8}=\frac{6}{11}[/tex]
Given a line with slope m then the slope of a line perpendicular to it is
[tex]$m_{\text {perpendicular }}=-\frac{1}{m}=-\frac{1}{\frac{-6}{11}}=-\frac{11}{6}$[/tex], then
[tex]$y=-\frac{11}{6} x+c[/tex] is the partial equation
To find c substitute A(3,8) into the partial equation
[tex]$9=-\frac{-11}{6}+C[/tex]
[tex]$-\left(-\frac{11}{6}\right)+C=9$[/tex]
Apply rule -(-a)=a
[tex]$\frac{11}{6}+C=9$[/tex]
Subtract [tex]$\frac{11}{6}$[/tex] from both sides
[tex]$\frac{11}{6}+C-\frac{11}{6}=9-\frac{11}{6}$[/tex]
Simplify
[tex]$C=\frac{43}{6}$[/tex]
[tex]$y=-\frac{11}{6} x+\frac{43}{6}[/tex] be the equation of perpendicular line.
Therefore, the value of c = 43/6.
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