Question #af25e

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Question #af25e

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Answer 1 · 2016-10-09T19:30:17

$a = - 6$ $a=-6$

Explanation:

Since these two lines meet at a right angle that means these two lines are perpendicular.
Two lines are perpendicular if the product of their slopes is -1.

That is two straight lines $y = a x + b and y_{1} = a_{1} x + b_{1}$ $color(red)(y=ax+b) and color(blue)(y_1=a_1x+b_1$ are perpendicular if $a \cdot a_{1} = - 1$ $color(green)(a*a_1=-1)$

Here we have:

Equation of the First straight line:
$2 y + x + 3 = 0$ $2y+x+3=0$
$2 y = - x - 3$ $2y=-x-3$
$y = - \frac{x}{2} - \frac{3}{2}$ $color(red)(y=-x/2-3/2$
Here the slope is $- \frac{1}{2}$ $color(red)(-1/2)$

Equation of the second is:
$3 y + a x + 2 = 0$ $3y+ax+2=0$
$3 y = - a x - 2$ $3y=-ax-2$
$y = - \frac{a}{3} x - \frac{2}{3}$ $color(blue)(y=-a/3x-2/3$
Here the slope is $- \frac{a}{3}$ $color(blue)(-a/3)$

These two lines are perpendicular that is :
$- \frac{1}{2} \cdot - \frac{a}{3} = - 1$ $color(red)(-1/2)*color(blue)(-a/3)=-1$
$\frac{a}{6} = - 1$ $a/6=-1$
$a = - 6$ $a=-6$

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Question #af25e

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