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.
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