Find equation of line passes from point of intersection of $3 x + 4 y = 7$ and $x - y + 2 = 0$ . whose slope is $5$ .

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Solution

equation of line :- $(3 x + 4 y = 7)$ & $x - 4 = - 2$
slope is 5
$\to$ solve the $(3 x + 4 y = 7)$ & $x - 4 = - 2$
$3 x + 4 y = 7$
$4 x - 4 y = - 8$
____________
$7 x = - 1$
$x = - 1 / 7$
$\to - \frac{1}{7} - y = - 2$
$y = 2 - 1 / 7$
$y = \frac{13}{7}$
$\to$ equation of line passing
$(- 1 / 7, 11 / 7)$ & slope is 5
$\frac{y - y_{1}}{x - x_{1}} = m$
$y - 13 / 7 = 5 (x + 1 / 7)$
$y - 13 / 7 = 5 x + 5 / 7$
$7 y - 13 = 35 x + 5$
$35 x - 7 y + 18 = 0$ Ans

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