Question

Find the equation of the line passing through the origin and parallel to line AB, where A
is (2, 4) and B is (1, 7).

Answer 1

Answer:

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Step-by-step explanation:

$so \: here \: for \: line \: AB \\ let \: then \\ A = (x1,y1) = (2,4) \\ B = (x2,y2) = (1,7) \\ \\ so \: hence \: then \\ \\ slope \: of \: line \: AB \: (m)= \frac{y2 - y1}{x2 - x1} \\ \\ = \frac{7 - 4}{1 - 2} \\ \\ = \frac{3}{( - 1)} \\ \\ = - 3 \\ \\ so \: as \: the \: other \: line \: | | \: AB \\ slope \: of \: that \: line \: = slope \: of \: AB \\ = - 3$

$so \: we \: know \: that \\ slope - point \: form \: equation \: of \: \\ straight \: line \: is \: given \: by \\ y - y1 = m(x - x1) \\ \\ as \: the \: other \: line \: passes \: through \: origin \\ let \: then \\ (x1,y1) = (0,0) \\ \\ thus \: then \\ \\ y - 0 = - 3(x - 0) \\ y = - 3x \\ 3x + y = 0$