Question

What is the equation of the line perpendicular to `y - 4 = 0` and passing through (-1, 6)? Please show working.

Answer 1

`x=-1`

Explanation:

`"note that "y-4=0" can be expressed as "y=4`

`"This is a horizontal line parallel to the x-axis passing "`
`"through all points in the plane with a y-coordinate "=4`

`"A line perpendicular to "y=4" must therefore be a "`
`"vertical line parallel to the y-axis"`

`"such a line has equation "x=c" where c is the value"`

`"of the x-coordinate the line passes through"`

`"here the line passes through "(-1,6)`

`"the equation of the perpendicular line is therefore"`

`color(red)(bar(ul(|color(white)(2/2)color(black)(x=-1)color(white)(2/2)|)))`
graph{(y-0.001x-4)(y-1000x-1000)=0 [-10, 10, -5, 5]}