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

Sagot :

Theekshana

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]

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