Question

Arthur is trying to find the equation of a perpendicular to y = 1 over 4x + 4 in slope-intercept form that passes through the point (−2, 6). Which of the following equations will he use?

y − 6 = 1 over 4(x − (−2))
y − (−2) = 1 over 4(x − 6)
y − 6 = −4(x − (−2))
y − (−2) = −4(x − 6)

Answer 1

y − 6 = −4(x − (−2))

Explanation:

We have an equation of a line
`y=(1)/(4) x+4` which passes through the point (-2, 6).

The standard form of an equation is
`y = mx+c`

so in the given equation, we have a slope of
`(1)/(4)` so the slope of the perpendicular line will be
`-4` since its the negative reciprocal of the line.

So putting these values in the equation (y - y1) = m (x - x1), we get:

`y-6=--4(x - (-2) )`

Therefore, the correct answer option is y − 6 = −4(x − (−2)).

Answer 2

C) y − 6 = −4(x − (−2))

Explanation:

The given equation is y = 1/4 x + 4 and passes through the point (-2, 6)

We have to find the perpendicular line.

The slope of the perpendicular line is the negative reciprocal of the given slope of the line.

The given slope of the line is 1/4,

The slope of the perpendicular line is -4.

It is passes through the point (-2, 6)

The formula is (y - y1) = m (x - x1)

Here x1 = -2 and y1 = 6 and m = -4

Plug in those values into the formula, we get

y - 6 = -4(x -(-2))

Therefore, the answer is C) y − 6 = −4(x − (−2))

Thank you.