Question

Indicate in standard form the equation of the line passing through the given points.

Answer 1

The equation of the line passing through the given points S(1/2, 1), T(1/2,4) would be 2y = 3x - 1/2.

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

$(y - y_1) = \dfrac{y_2 - y_1}{x_2 - x_1} (x -x_1)$

The equation of the line passes through the given points.

S(1/2, 1), T(1/2,4)

Then the equation ;

$(y - y_1) = \dfrac{y_2 - y_1}{x_2 - x_1} (x -x_1)\\\\(y - 1/2) = \dfrac{4 - 1}{1-1/2} (x -1/2)\\\\(y - 1/2) = \dfrac{3}{1/2} (x -1/2)\\\\2(y - 1/2) = 3(x -1/2)\\\\2y -1 = 3x - 3/2\\\\2y = 3x -1/2$

The equation of the line passing through the given points S(1/2, 1), T(1/2,4) would be 2y = 3x - 1/2.

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