Question

(-1, -7), 3x + 12y = -6 find the perpendicular line

Answer 1

Explanation:

write equation in terms of x

y=(-6+3x)/12

from this equation u can see your gradient is 3/12 or 1/4

your perpendicular gradient is -1/m (m being the gradient of your main line)

so gradient of perpendicular= -4

since coordinate of main line is given, that point will also be on perpendicular.

so u have point and gradient so u can Calculate line equation

Y=MX+C

(-7)=(-4)(-1)+c

c=-11

y=-4x-11

^equation of perpendicular

Answer 2

`\[y=4x-3\]`

Explanation:

Equation of the given line:
`\[3x+12y=-6\]`

Rewriting it in standard form:
`\[12y=-3x-6\]`

=>
`\[y=-(3)/(12)x-(6)/(12)\]`

Or,
`\[y=-(1)/(4)x-(1)/(2)\]`

Slope of the line =
`\[-(1)/(4)\]`

Slope of the perpendicular line = 4

So the equation of the perpendicular line:

`\[y=4x+c\]`

This passes through the point (-1,-7).Substituting in the equation:

`\[-7=4*(-1)+c\]`

=>
`\[c=-7+4\]`

=>
`\[c=-3\]`

So the equation of the line :

`\[y=4x-3\]`