Question

what �is the equation of a line that is perpendicular to the line  y = − 2 5 x − 5 y = - 2 5 x - 5 and passes through the point  ( 6 , 1 )

Answer 1

Answer:

$y=\frac{1}{25}x-\frac{31}{25}$

Step-by-step explanation:

$y=-25x-5$

You can get the gradient of the line perpendicular to this as you know the products of their gradients will be -1.

$-25*m_{perpendicular}=-1\\m_{perpendicular}=\frac{1}{25}$

We have a gradient, and a point (6, 1), so we can now substitute our known values into the line equation.

$(y-y_0)=m(x-x_0)$

$y-1=\frac{1}{25} (x-6)$

Rearrange for y and collect terms.

$y=\frac{1}{25}x-\frac{6}{25}-1\\\\y=\frac{1}{25}x-\frac{31}{25}$