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Sagot :
Given:
The equation of line is,
[tex]y=-\frac{x}{3}-8[/tex]As given that the required line is perpendicular to the above line.
It means the slope of required line will be negative reciprocal of above line.
[tex]\begin{gathered} y=-\frac{x}{3}-8 \\ \text{Compare it with y=mx+b} \\ \Rightarrow m=-\frac{1}{3} \end{gathered}[/tex]The slope of the required line will be,
[tex]m_1=-\frac{1}{m}=-\frac{1}{-\frac{1}{3}}=3[/tex]Now, given that the required line passing through point (7,-3) .
[tex]\begin{gathered} y=m_1x+b \\ (x,y)=(7,-3) \\ -3=3(7)+b \\ b=-24 \end{gathered}[/tex]The slope-intercept form is,
[tex]\begin{gathered} y=m_1x+b \\ y=3x-24 \end{gathered}[/tex]
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