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What is the equation, in slope-intercept form, of the line that is perpendicular to the line y-4= -2/3 (x-6) and passes through the point (-2, -2)?
Oy=-2/3x-10
Oy=-2/3x+10
Oy=x3/2x-1
O y=3/2x+1

What is the equation in slopeintercept form of the line that is perpendicular to the line y4 23 x6 and passes through the point 2 2 Oy23x10 Oy23x10 Oyx32x1 O y3 class=

Respuesta :

Stephen46

Answer:

The answer is option D.

Equation of a line is y = mx + c

m = slope

c = intercept on y axis

y-4= -2/3 (x-6)

y = -2/3x + 4 + 4

y = -2/3x + 8

From the above equation

m= -2/3

Since the lines are perpendicular the slope of the line is the negative inverse of the original line.

so m = 3/2

Equation of the line using point (-2 , -2) is

y + 2 = 3/2(x+2)

y = 3/2x + 3 - 2

y = 3/2x + 1

That's the last option

Hope this helps

The linear equation with the given characteristics is given by:

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

What is the equation of a line in slope-intercept form?

It is given by:

y = mx + b.

In which:

  • m is the slope.
  • b is the y-intercept.

When two lines are perpendicular, the multiplication of their slopes is -1, hence:

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

[tex]2m = 3[/tex]

[tex]m = \frac{3}{2}[/tex]

Then:

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

It passes through the point (-2, -2), hence:

[tex]-2 = \frac{3}{2}(-2) + b[/tex]

[tex]-3 + b = -2[/tex]

[tex]b = 1[/tex]

Hence, the equation is:

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

More can be learned about linear equations at https://brainly.com/question/24808124

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