Question

Line j is perpendicular to the line with the given equation and line j passes through P. How do I write an equation of line j on the givens below? (A) `y=1/3x+4, P(0, 5)` (B) `y=3x+4, P(0, -2)` (C) `y= -4/5x+4, P(1, 1)` (D) `y=2/3x+4, P(2, 0)`

emphasized text

Answer 1

Please see below.

Explanation:

The slope pf a line perpendicular to a given line whose slope is `m` is `-1/m`. So, if a line is given in slope intercept form say `y=mx+c`, its slope is `m` and that of line perpendicular to it is `-1/m`, i.e. reciprocal with change of sign.

Now using point slope form of equation, equation of line perpendicular to `y=mx+c` and passing through `(x_1,y_1)` is `y-y_1=-1/m(x-x_1)`.

Using this

(A) The slope of a line perpendicular to `y=1/3x+4` is `-3` and equation of line perpendicular to it passing through `P(0,5)` is `y-5=-3(x-0)` or `y=-3x+5`

(B) The slope of a line perpendicular to `y=3x+4` is `-1/3` and equation of line perpendicular to it passing through `P(0,-2)` is `y-(-2)=-1/3(x-0)` or `y=-1/3x-2`

(C) The slope of a line perpendicular to `y=-4/5x+4` is `5/4` and equation of line perpendicular to it passing through `P(1,1)` is `y-1=5/4(x-1)` or `4y-4=5x-5`

(D) The slope of a line perpendicular to `y=2/3x+4` is `-3/2` and equation of line perpendicular to it passing through `P(2,0)` is `y-0=-3/2(x-2)` or `y=-3/2x+3`