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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)?
O y=-2/3x-10/3
Oy=-2/3x+10/3
O y=3/2x-1
O y=3/2x+1

What is the equation in slopeintercept form of the line that is perpendicular to the line y4 23x 6 and passes through the point 2 2 O y23x103 Oy23x103 O y32x1 O class=

Respuesta :

Answer:

y=3/2x+1

Step-by-step explanation:

I used the website desmos and put in the equation y-4=-2/3(x-6) with the point (-2,-2) then put in the equations to see what matched up. y=3/2x+1 was both perpendicular to y-4=-2/3(x-6) and passed through the point (-2,-2).

The equation in slope-intercept formula of the desired line is given by:

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

What is a linear function?

A linear function is modeled by:

y = mx + b

In which:

  • m is the slope, which is the rate of change, that is, by how much y changes when x changes by 1.
  • b is the y-intercept, which is the value of y when x = 0, and can also be interpreted as the initial value of the function.

The line is perpendicular to a line with slope -2/3, hence:

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

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

Hence:

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

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

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

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

b = 1.

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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