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Write an equation of the line that passes through a pair of points:
(2, 3), (4, negative 2)
a.
y = Negative five-halvesx – StartFraction 1 Over 8 EndFraction
c.
y = Negative five-halvesx + 8
b.
y = Negative five-halvesx – 8
d.
y = Five-halvesx + 8

Sagot :

The equation of line that passes through a pair of points: (2, 3), (4, -2).is option B. y = -5/2 x + 8.

What is the equation of a line passing through two given points in 2 dimensional plane?

Suppose the given points are (x_1, y_1) and (x_2, y_2),

then the equation of the straight line joining both two points is given by

[tex](y - y_1) = \dfrac{y_2 - y_1}{x_2 - x_1} (x -x_1)[/tex]

We need to find the equation of the line that passes through a pair of points: (2, 3), (4, -2).

So, the equation would be

[tex](y - y_1) = \dfrac{y_2 - y_1}{x_2 - x_1} (x -x_1)[/tex]

[tex](y - 3) = \dfrac{-2 - 3}{4- 2} (x -2)\\\\\\(y - 3) = \dfrac{-5}{2} (x -2)\\\\\\2(y - 3) = -5 (x -2)\\\\2y - 6 = -5x + 10\\\\2y = -5x + 16\\\\y = -5/2 x + 8[/tex]

Hence, the equation of line is option B. y = -5/2 x + 8.

Learn more about straight line equation here:

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Answer:B

Step-by-step explanation:

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