The equation $3 x-2 y=4$ is graphed in the $x y$-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: \(-1.5 * -0.6666666666666666 = 1.0\)

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