Answer:
[tex]y=-3x+8[/tex]
Step-by-step explanation:
[tex]-2x+6y=-4\\6y=2x-4\\y=\frac{1}{3}x+\frac{2}{3}\\[/tex]
if two lines perpendicular,
[tex]m_{1} .m_{2}=-1\\ \frac{1}{3} .m_{2}=-1\\m_{2}=-3[/tex]
the line perpendicular to this line is
[tex]y=-3x+k[/tex] ; k ∈ R
the line passes through the point (5,-7)
so,
[tex]-7=-3.(5)+k\\-7=-15+k\\k=8[/tex]
∴the equation of a line that passes through the point (5,-7) and is perpendicular to the line -2x+6y=-4 is
[tex]y=-3x+8[/tex]
