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

Answer:

$y=-3x+8$

Step-by-step explanation:

$-2x+6y=-4\\6y=2x-4\\y=\frac{1}{3}x+\frac{2}{3}$

if two lines perpendicular,

$m_{1} .m_{2}=-1\\ \frac{1}{3} .m_{2}=-1\\m_{2}=-3$

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

$y=-3x+8$