Respuesta :
Answer:
No, the lines are not perpendicular
Explanation:
Two lines are perpendicular if the multiplication of their slopes is equal to -1.
Therefore, we first need to identify the slopes of each equation:
For y = (2/3)x+1, the slope is 2/3 because it is the number beside the x.
On the other hand, to know the slope of the equation 3y + 2x = 4, we need to solve for y, so:
[tex]\begin{gathered} 3y+2x=4 \\ 3y+2x-2x=4-2x \\ 3y=-2x+4 \\ \frac{3y}{3}=\frac{-2x}{3}+\frac{4}{3} \\ y=-\frac{2}{3}x+\frac{4}{3} \end{gathered}[/tex]Therefore, the slope of the second equation is -2/3
Then, the multiplication of 2/3 by -2/3 is equal to:
[tex]\frac{2}{3}\times-\frac{2}{3}=\frac{2\times(-2)}{3\times3}=-\frac{4}{9}[/tex]Since -4/9 and -1 are distinct, the lines are not perpendicular.
