Answer:
[tex]\frac{2}{3}[/tex]
Step-by-step explanation:
• First rewrite the original equation in the form y = mx + c ,
where m = gradient:
[tex]3x + 2y = 7[/tex]
⇒ [tex]2y = -3x + 7[/tex]
⇒ [tex]y = \frac{-3}{2}x + \frac{7}{2}[/tex]
• From this equation, we can see that the gradient, m = [tex]\frac{-3}{2}[/tex] .
The gradient of a line perpendicular to another line with gradient m, = [tex]\frac{-1}{m}[/tex].
∴ gradient of perpendicular = -1 ÷ [tex]\frac{-3}{2}[/tex]
= [tex]\frac{2}{3}[/tex]
