Show that the lines are parallel
a) $2 x - 3 y + 7 = 0 a n d 12 y = 8 x - 5$

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Solution

For the general equation of straight line $a x + b y + c = 0$ , slope $m$ is given by

$m = - \frac{a}{b}$

One line is
$2 x - 3 y + 7 = 0$

slope, $m = - \frac{2}{- 3}$

$m = \frac{2}{3}$

Second line is,

$12 y = 8 x - 5$

$8 x - 12 y - 5 = 0$

slope, $m = - \frac{8}{- 12}$ $= \frac{2}{3}$

Slope of both the lines is equal, so the lines are parallel.

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Show that the point (3, -5) lies between the parallel lines $2 x + 3 y - 7 = 0$ and $2 x + 3 y + 12 = 0$ and find the equation of lines through (3, -5) cutting the above lines at an angle of $45^{\circ}$ .

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Show that the lines are parallel a) 2x−3y+7=0and12y=8x−5

For the general equation of straight line ax+by+c=0 , slope m is given bym=−abOne line is 2x−3y+7=0slope, m=−2−3m=23Second line is,12y=8x−58x−12y−5=0slope, m=−8−12=23Slope of both the lines is equal, so the lines are parallel.

Show that the lines are parallel
a) $2 x - 3 y + 7 = 0 a n d 12 y = 8 x - 5$