Question

WILL GIVE BRAINLIEST: If the graph of 2x+3y − 6=0 is perpendicular to the graph of ax − 3y=5. What is the value of a?

Answer 1

Answer:

a = $\frac{9}{2}$

Step-by-step explanation:

To find the value of a, find the Slope of both the equations.

For lines to be perpendicular to each other    $m_{1}m_{2} = - 1$

For line 1:

2x + 3y − 6 = 0 represent the line in y=mx +c form

3y = -2x + 6

y = $\frac{-2}{3} x$ + $\frac{6}{3}$

y = $\frac{-2}{3} x$ + 2

$m_{1}$ = $\frac{-2}{3}$

For line 2:

ax - 3y = 5

ax = 5 + 3y

ax - 5 = 3y

y = $\frac{ax}{3} - \frac{5}{3}$

$m_{2}$ = $\frac{a}{3}$

Apply the condition of perpendicularity:

$\frac{-2}{3}$ * $\frac{a}{3}$ = - 1

$\frac{2a}{9} = 1$

a = $\frac{9}{2}$