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the point-slope form of the equation of the line that passes through (–4, –3) and (12, 1) is y – 1 = (x – 12). what is the standard form of the equation for this line? x – 4y = 8 x – 4y = 2 4x – y = 8 4x – y = 2

Respuesta :

nobillionaireNobley
(y - 1) = 1/4(x - 12)
4(y - 1) = x - 12
4y - 4 = x - 12
x - 4y = -4 + 12
x - 4y = 8

Answer:  The correct option is

(A) [tex]x-4y=8.[/tex]

Step-by-step explanation:  Given that the point-slope form of the equation of the line passing through the points (-4, -3) and (12, 1) is given by

[tex]y-1=\dfrac{1}{4}(x-12)~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~(i)[/tex]

We are to select the correct standard form of the equation for the above line.

From equation (i), we have

[tex]y-1=\dfrac{1}{4}(x-12)\\\\\\\Rightarrow 4(y-1)=x-12\\\\\Rightarrow 4y-4=x-12\\\\\Rightarrow x-12-4y+4=0\\\\\Rightarrow x-4y-8=0\\\\\Rightarrow x-4y=8.[/tex]

Thus, the required standard form of the equation of the line is

[tex]x-4y=8.[/tex]

Option (A) is CORRECT.

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