What is the equation of the line passing through $(3, - 4)$ $(3,-4)$ and $(- 5, - 1)$ $(-5,-1)$ ?

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Answer 1 · 2016-12-18T17:17:12

4x + 8y + 20 = 0

we know equation of a line passing through $(x_{1}, y_{1}) and (x_{2}, y_{2})$ $(x_1,y_1) and (x_2, y_2)$

= $\frac{y - y_{1}}{x - x_{1}} = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$ $[y-y_1]/[x-x_1] = [y_2-y_1]/[x_2-x_1]$

So equation of line passing through (3, -4) and (-5, -1) =

$\frac{y - (- 4)}{x - 3} = \frac{- 1 - (- 4)}{- 5 - 3}$ $[y-(-4)]/[x-3] = [-1-(-4)]/[-5-3]$

or, $\frac{y + 4}{x - 3} = \frac{- 1 + 5}{- 8}$ $[y+4]/[x-3] = [-1+5]/[-8]$

or, $- 8 (y + 4) = 4 (x - 3)$ $-8(y+4) = 4(x-3)$

or, $- 8 y - 32 = 4 x - 12$ $-8y-32 = 4x-12$

or, 4x + 8y + 32 - 12 = 0

or, 4x + 8y + 20 = 0

What is the equation of the line passing through (3,-4)(3,−4)(3,-4) and (-5,-1)(−5,−1)(-5,-1)?