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Find an equation of the line passing through the point ( 6 , − 4 ) (6,-4) and perpendicular to 9 x − 3 y = 9 9x-3y=9 . Write your answer in slope-intercept form.

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nkirotedoreen46

Answer:

[tex]y =-\frac{1}{3}-2[/tex]

Step-by-step explanation:

We are given;

  • A point (6, -4)
  • An equation of a line, 9x - 3y = 9

We are required to determine the equation a line passing through a point (6, -4) and perpendicular to the given line;

  • To answer the question we need to get the gradient of the given line first.
  • We write the equation 9x - 3y = 9  in the form of y = mx + c, where m is the slope;
  • That is;

y = 3x -3

  • Thus, the slope of the line is 3

But; m₁ × m₂ = -1 (For perpendicular lines)

Therefore;

m₂ = -1 ÷ 3

    = -1/3

Therefore, the slope of the line in question is -1/3 and the line passes through (6, -4).

To get its equation, we get another point (x, y)

Then;

[tex]\frac{y+4}{x-6}=\frac{-1}{3}[/tex]

Thus;

[tex]3(y+4) = -1(x-6)\\3y + 12 = -x+6[/tex]

In the form of slope-intercept, the equation will be;

[tex]3y = -x - 6\\y =-\frac{1}{3}-2[/tex]

Thus, the equation of the line is;

[tex]y =-\frac{1}{3}-2[/tex]

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