Question

Which of the following equations is parallel to the graphed line? (1 point)
y=−3/2x−1
y=−2/3x+2
y=2/3x+3
y=3/2x−7

Answer 1

To determine which equation is parallel to the given line \(y = -\frac{3}{2}x - 1\), we need to find a line that has the same slope.

The slope of the given line is \(-\frac{3}{2}\).

Now, let's look at the slopes of the options provided:

1. \(y = -\frac{3}{2}x - 1\) (slope = \(-\frac{3}{2}\))
2. \(y = -\frac{2}{3}x + 2\) (slope = \(-\frac{2}{3}\))
3. \(y = \frac{2}{3}x + 3\) (slope = \(\frac{2}{3}\))
4. \(y = \frac{3}{2}x - 7\) (slope = \(\frac{3}{2}\))

The only equation that has the same slope of \(-\frac{3}{2}\) is:

**\(y = -\frac{3}{2}x - 1\)**

However, since they are the same line, the equations that we are looking for are distinct. None of the other equations have a slope of \(-\frac{3}{2}\), therefore the final answer does not have a parallel line in the list provided.

To summarize, while none of the options are parallel to the original line \(y = -\frac{3}{2}x - 1\) besides the line itself, you should double-check the equations if looking for a different condition or another mathematical context that may yield a different parallel result elsewhere.