Question

find the equation of the line passing through the point (-4,1) and the perpendicular to the line y=1/3x+4

Answer 1

The answer is

`y = - 3x - 11`

Explanation:

Equation of a line is y = mx + c

where

m is the slope

c is the y intercept

From the question

`y = (1)/(3) x + 4`

Comparing it with the general equation above

Slope / m = 1/3

Since the lines are perpendicular to each other the slope of the other line is the negative inverse of the original line

That's

Slope of perpendicular line = - 3

Equation of the line using point (-4 , 1) and slope - 3 is

`y - 1 = - 3(x + 4) \\ y - 1 = - 3x - 12 \\ y = - 3x - 12 + 1`

We have the final answer as

y = - 3x - 11

Hope this helps you