The equation $3x-2y=4$ is graphed in the $xy$-plane. Which of the statements is true of its graph?
Choose 1 answer:
INCORRECT
The graph is a line parallel to the line whose equation is
$$y=-\frac{2}{3}x+1$$
The slope of this line is $-\frac{2}{3}$, so the lines are not parallel.
CORRECT (SELECTED)
The graph is a line perpendicular to the line whose equation is
$$y=-\frac{2}{3}x+1$$

Step 1 ：The given equation is in the form of a linear equation, i.e., $ax+by=c$. The slope of a line in this form is given by $-a/b$. So, the slope of the given line is $-3/2$.

Step 2 ：The slope of the line $y=-2/3x+1$ is $-2/3$.

Step 3 ：Two lines are perpendicular if the product of their slopes is $-1$. So, we need to check if the product of the slopes of the two lines is $-1$.

Step 4 ：Calculate the product of the slopes: $-1.5\ast -0.6666666666666666=1.0$

Step 5 ：The product of the slopes of the two lines is 1.0, which is not equal to -1. Therefore, the two lines are not perpendicular to each other.

Step 6 ：$\boxed{{\displaystyle \text{The graph of the equation }3x-2y=4\text{ is not a line perpendicular to the line whose equation is }y=-\frac{2}{3}x+1}}$