Question

Two perpendicular lines intersect on the y -axis. The equation of one line is x + 4y - 24 = 0 . Determine the equation of the other line.

Answer 1

Rearrange the equation into standard form:
x+4y-24=0
bring y over to the other side
x-24=-4y
divide both sides by -4
`y=- (x)/(4)+6`
We see that the y-intercept is (0,6) (through y=mx+b)
The formula for perpendicular lines is
`m_(1) × m_(2) =-1`, and they must have a common coordinate (this will be (0,6), the y-intercept).
-1÷-x/4=4x, so the slope of the second line will be 4x. The y-intercept doesn't change as the lines share a common coordinate, so the final equation of the second equation is y+4x+6

Answer 2

Intersecting on the y axis means x=0.
Plug x=0 in the equation to find out the y value of the intercept> 0+4y-24=0, y=6
so the both line passes the point (0,6)

two perpendicular lines have slopes that are negative reciprocals of each other, that is, if one slope is a/b, the other is -b/a

In this case, the line x+4y-24=0, 4y=-x+24, y=-1/4 x + 6, the slope is -1/4, so the slope of the perpendicular line is 4/1.

the equation is y=4x+6