Question

find the equation of the line that is perpendicular to the line y=-4x-4) and passes through the line (-1,8)

Answer 1

Explanation:

We know that the product of slopes of two perpendicular lines is -1 . So the slope of the line perpendicular to the given line will be negative reciprocal of the slope of the given line. The given line is,

`\implies \rm y = -4x -4`

on comparing it to the slope intercept form of the line we have,

`\implies \rm m =-4\ (slope)`

so the slope of the perpendicular line would be,

`\implies \rm m_(\perp)=(1)/(4)`

Now we may use the point slope form of the line ro to find out the equation of the line that passes through the given point as ,

`\implies \rm y - y_1 = m(x-x_1)\\`

`\implies \rm y -8=(1)/(4)\{ x -(-1)\}\\`

`\implies \rm 4y -32 = x +1\\`

`\implies \rm x-4y +33=0`

and we are done!

-rishabh