Answer:
[tex]y = - \frac{2}{3}x - 3 [/tex]
Step-by-step explanation:
The equation of line q: y = 3x + 5 has gradient 3.
If the line p is perpendicular to line q, then the gradient of p = - 1/3, since the p contains (6,5)
The equation of line p :
[tex] - \frac{1}{3} = \frac{y - ( - 5)}{x - 6} [/tex]
[tex] - \frac{1}{3} = \frac{y + 5}{x - 6} [/tex]
3(y + 5) = -1 (x - 6)
3y + 15 = -2x + 6
3y = - 2x + 6 - 15
3y = - 2x - 9
Divide both sides by 3
[tex]y = - \frac{2}{3}x \: - 3[/tex]
