Answer:
[tex]y = \frac{1}{3}x - 9[/tex]
Step-by-step explanation:
Standard equation of a line is y = mx + b, where m is the slope.
Given line y = - 3x + 78, slope, m₁ = -3
To find the line perpendicular to the given line.
The lines are perpendicular to each other if the product of their slopes = - 1
That is,
[tex]m_1 \times m_2 = -1[/tex]
So the slope of new line is
[tex]-3 \times m_2 = -1\\\\m_2 = \frac{-1}{-3} = \frac{1}{3}[/tex]
[tex]Therefore , equation \ of \ new \ line \ \\\\(y - y_1) = m_2(x - x_1) , where \ (x_1 , y_1) = (9, -6 )\\\\(y - (-6))= \frac{1}{3}(x -9)\\\\y + 6 = \frac{1}{3} x - 3\\\\y = \frac{1}{3}x -3-6\\\\y = \frac{1}{3}x -9\\\\[/tex]
