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What is the equation, in slope-intercept form, of the line that is perpendicular to the line
y – 4 = –Two-thirds(x – 6) and passes through the point (−2, −2)?

Respuesta :

nkirotedoreen46

Answer:

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

Step-by-step explanation:

We are given;

The equation of a line;

[tex]y-4 = -\frac{2}{3}(x-6)[/tex]

We are required to determine the equation of a line perpendicular to the above line and passing through (-2, -2).

  • We can get the gradient of a line when given its gradient and a point where it is passing through.
  • In this case;

We need to know that the product of gradient of two parallel lines is -1

  • Therefore, we can get the gradient of the unknown line;

m₁× m₂ = -1

Thus;

m₂ = -1 ÷ -2/3

     = 3/2

Thus, the gradient is 3/2 and the line passes through (-2,-2)

Thus, to get its equation, we take another point (x,y)

We get;

[tex]\frac{y+2}{x+2}= \frac{3}{2}[/tex]

Then;

[tex]2(y+2)=3(x+2\\2y + 4 = 3x + 6[/tex]

Combining the like terms,

[tex]2y=3x+2[/tex]

In the form of slope-intercept;

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

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