# How do you write the equation in point slope form given (5,-6) and perpendicular to the line whose equation is x-7y=3?

Apr 7, 2016

$\implies y + 6 = - 7 \left(x - 5\right)$

#### Explanation:

Point slope format : $y - {y}_{1} = m \left(x - {x}_{1}\right)$

Given:$\text{ } x - 7 y = 3$

In standard form this is $y = \frac{1}{7} x - \frac{3}{7}$

So the gradient of the perpendicular line is of form: $\left(- 1\right) \times \frac{1}{m}$

$\implies \text{ required gradient } = - 7$

So standard form of the new equation is

$y = - 7 x + c$

We are given the point $\left(x , y\right) \to \left(5 , - 6\right)$

So in slope point form we have

$y - \left(- 6\right) = - 7 \left(x - 5\right)$

$\implies y + 6 = - 7 \left(x - 5\right)$