Question

Write the equation of a line that passes through the point (5,-7) and is perpendicular to the line -2x+6y=-4

Answer 1

`y=-3x+8`

Step-by-step explanation:

`-2x+6y=-4\\6y=2x-4\\y=(1)/(3)x+(2)/(3)\\`

if two lines perpendicular,

`m_(1) .m_(2)=-1\\ (1)/(3) .m_(2)=-1\\m_(2)=-3`

the line perpendicular to this line is

`y=-3x+k` ; k ∈ R

the line passes through the point (5,-7)

so,

`-7=-3.(5)+k\\-7=-15+k\\k=8`

∴the equation of a line that passes through the point (5,-7) and is perpendicular to the line -2x+6y=-4 is

`y=-3x+8`