Question

Find the equation of the line that is perpendicular to the line y = 4 and passes through the point (−2, 1).

A) x = −2
B) y = −1
C) y = 1
D) x = 2

Answer 1

A

Explanation:

y = 4 is a horizontal line parallel to the x- axis with a slope of zero

A line perpendicular to it is a vertical line parallel to the y- axis

The equation of a vertical line is x = c

where c is the value of the x- coordinates the line passes through.

The line passes through (- 2, 1) with x- coordinate - 2, hence

x = - 2 ← equation of perpendicular line → A

Answer 2

A.
`x=-2`

Explanation:

We are asked to find the equation that is perpendicular to line
`y=4` and passes through the point
`(-2,1)`.

We can see that our given equation is a horizontal line, which crosses y-axis at point
`(0,4)`.

Every vertical line is perpendicular to a horizontal line. We know that equation of a vertical line is in form
`x=a`, which crosses x-axis at point
`(a,0)`.

Since we need to find the equation that passes through point
`(-2,1)`, so our required equation will pass x-axis at
`-2`.

Therefore, our required equation would be
`x=-2` and option A is the correct choice.