Respuesta :

MamoonWasim

Step-by-step 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:

[tex]\[y=4x-3\][/tex]

Step-by-step explanation:

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

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

=> [tex]\[y=-\frac{3}{12}x-\frac{6}{12}\][/tex]

Or, [tex]\[y=-\frac{1}{4}x-\frac{1}{2}\][/tex]

Slope of the line = [tex]\[-\frac{1}{4}\][/tex]

Slope of the perpendicular line = 4

So the equation of the perpendicular line:

[tex]\[y=4x+c\][/tex]

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

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

=> [tex]\[c=-7+4\][/tex]

=> [tex]\[c=-3\][/tex]

So the equation of the line :

[tex]\[y=4x-3\][/tex]

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