The equation of the line passing through given pair of points $(- 3, 5)$ and $(4, - 7)$ given in the form $y = m x + c$ is,

y = \frac{12}{7} x + \frac{1}{7}

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y = \frac{12}{7} x - \frac{1}{7}

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y = - \frac{12}{7} x - \frac{1}{7}

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y = - \frac{12}{7} x + \frac{1}{7}

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Solution

The correct option is C $y = - \frac{12}{7} x - \frac{1}{7}$
The equation of a line passing through two points $(x_{1}, y_{1})$ & $Q (x_{2}, y_{2})$ is $\frac{y - y_{1}}{y_{2} - y_{1}} = \frac{x - x_{1}}{x_{2} - x_{1}}$ .

The equation of line passing through $(- 3, 5)$ and $(4, - 7)$ is:

$\frac{y - 5}{- 7 - 5} = \frac{x + 3}{4 + 3}$

$7 (y - 5) = - 12 x$

$7 y - 35 = - 12 x - 36$

$7 y = - 12 x - 1$

$y = \frac{- 12}{7} x - \frac{1}{7}$

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The equation of the line passing through given pair of points (−3,5) and (4,−7) given in the form y=mx+c is,

The correct option is C y=−127x−17The equation of a line passing through two points (x1,y1) & Q(x2,y2) is y−y1y2−y1=x−x1x2−x1.The equation of line passing through (−3,5) and (4,−7) is:y−5−7−5=x+34+37(y−5)=−12x7y−35=−12x−367y=−12x−1y=−127x−17

The equation of the line passing through given pair of points $(- 3, 5)$ and $(4, - 7)$ given in the form $y = m x + c$ is,