The equation of the line passing through point $P (0, 6)$ and slope $m = \frac{6}{7}$ is,

6 x - 7 y + 6 = 0

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7 x - 6 y + 42 = 0

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6 x - 7 y + 42 = 0

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6 x - 7 y - 42 = 0

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Solution

The correct option is C $6 x - 7 y + 42 = 0$
The line passing through point $P (a, b)$ and slope $m$ is given by
$(y - b) = m (x - a)$
Thus, here line passing through $(0, 6)$ with slope $\frac{6}{7}$ is given by:
$(y - 6) = \frac{6}{7} (x - 0)$
$7 (y - 6) = 6 x$
$6 x - 7 y + 42 = 0$

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The equation of the line passing through point P(0,6) and slope m=67 is,

The correct option is C 6x−7y+42=0The line passing through point P(a,b) and slope m is given by(y−b)=m(x−a)Thus, here line passing through (0,6) with slope 67 is given by:(y−6)=67(x−0)7(y−6)=6x6x−7y+42=0

The equation of the line passing through point $P (0, 6)$ and slope $m = \frac{6}{7}$ is,

The correct option is C $6 x - 7 y + 42 = 0$
The line passing through point $P (a, b)$ and slope $m$ is given by
$(y - b) = m (x - a)$
Thus, here line passing through $(0, 6)$ with slope $\frac{6}{7}$ is given by:
$(y - 6) = \frac{6}{7} (x - 0)$
$7 (y - 6) = 6 x$
$6 x - 7 y + 42 = 0$