Respuesta :

gmany

The point-slope form of line:

[tex]y-y_1=m(x-x_1)[/tex]

The fomula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

Substitute the coordinates of the points:

[tex]m=\dfrac{-4-2}{1-(-2)}=\dfrac{-6}{1+2}=\dfrac{-6}{3}=-2[/tex]

[tex]y-(-4)=-2(x-1)[/tex]       use distributive property

[tex]y+4=-2x+2[/tex]      subtract 4 from both sides

[tex]\boxed{y=-2x-2}[/tex]

SociometricStar

Answer:

y = -2x-2

Step-by-step explanation:

The line passes through the points (-2, 2) and (1, -4).

The slope of the line is given by

[tex]m=\frac{y_2-y_1}{x_2-x_1}\\\\m=\frac{-4-2}{1+2}\\\\m=\frac{-6}{3}\\\\m=-2[/tex]

The slope intercept form of a line is given by

y = mx +b, where m is the slope and b is the y-intercept.

We have, m = -2. Hence, the equation is

y = -2x + b

Now, use the point (-2,2) to find b

2 = -2(-2) + b

2 = 4 +b

b = -2

Hence, the equation of the line is y = -2x-2

Third option is correct.

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