Question

On a coordinate plane, a line goes through (negative 2, negative 4) and (2, 2). A point is at (negative 3, 1).
What is the equation, in point-slope form, of the line that is parallel to the given line and passes through the point (−3, 1)?

y – 1=Negative three-halves(x + 3)
y – 1=Negative two-thirds(x + 3)
y – 1= Two-thirds(x + 3)
y – 1= Three-halves(x + 3)

Answer 1

To determine the equation of the line that is parallel to the given line and passes through the point \((-3, 1)\), we first need to find the slope of the given line.

### Step 1: Find the slope of the given line

The given points on the line are:
- Point 1: \((-2, -4)\)
- Point 2: \((2, 2)\)

The slope \(m\) can be calculated using the formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Substituting in our points:
\[
m = \frac{2 - (-4)}{2 - (-2)} = \frac{2 + 4}{2 + 2} = \frac{6}{4} = \frac{3}{2}
\]

### Step 2: Write the equation in point-slope form

Since parallel lines have the same slope, the slope of the line we are looking for is also \(\frac{3}{2}\).

Using the point-slope form of the equation of a line:
\[
y - y_1 = m(x - x_1)
\]
where \((x_1, y_1)\) is the point \((-3, 1)\) and \(m = \frac{3}{2}\):
\[
y - 1 = \frac{3}{2}(x + 3)
\]

Thus, the equation of the line in point-slope form that is parallel to the given line and passes through the point \((-3, 1)\) is:
\[
y - 1 = \frac{3}{2}(x + 3)
\]

### Conclusion

None of the options given in the original question exactly match this equation. The correct answer for the equation of the line you have requested is:
\[
y - 1 = \frac{3}{2}(x + 3)
\]