Question

how do you write the equation of a line if you know its y-intercept and the equation of a line to which it is perpendicular ?

Answer 1

if you are writing it in the form y = mx + c
then you know that c it the y-intercept m the gardient

if you know the gradient of the peropendicular line then reciprocate that gradient and multiply it by - 1 to get the gradient.

e.g. gradient of perpen. = 2 and y intercept = 9

then gradient of line = -
`(1)/(2)`

Thus equation would be y = -
`(1)/(2)` x + 9

Answer 2

For a perpendicular line, you use the negative reciprocal. Meaning if you wanted the perpendicular slope of 5/3 you would get -3/5. And the y-intercept is you last portion. Say your equation to a perpendicular line is y=-3/4x-7 and your y-intercept is 5 then your other equation would be y=4/3x+5.