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We are asked to write the equation of a line passing through the point \((-4, -4)\) and parallel to the line given by the equation \(y = \frac{3}{2}x - 1\).

### Step 1: Identify the slope
The line \(y = \frac{3}{2}x - 1\) is in slope-intercept form \(y = mx + b\), where \(m\) is the slope. From the equation, the slope \(m = \frac{3}{2}\).

Since the new line is parallel to the given line, it will have the same slope, i.e., \(m = \frac{3}{2}\).

### Step 2: Use the point-slope form
The point-slope form of a line is:
\[
y - y_1 = m(x - x_1)
\]
where \((x_1, y_1)\) is the point the line passes through and \(m\) is the slope. Substituting \((-4, -4)\) for \((x_1, y_1)\) and \(\frac{3}{2}\) for \(m\), we get:
\[
y - (-4) = \frac{3}{2}(x - (-4))
\]
Simplifying:
\[
y + 4 = \frac{3}{2}(x + 4)
\]

### Step 3: Distribute the slope
Now distribute the \(\frac{3}{2}\) on the right-hand side:
\[
y + 4 = \frac{3}{2}x + \frac{3}{2} \times 4
\]
\[
y + 4 = \frac{3}{2}x + 6
\]

### Step 4: Solve for \(y\)
Subtract 4 from both sides to get the equation in slope-intercept form:
\[
y = \frac{3}{2}x + 6 - 4
\]
\[
y = \frac{3}{2}x + 2
\]

Thus, the equation of the line passing through the point \((-4, -4)\) and parallel to \(y = \frac{3}{2}x - 1\) is:
\[
y = \frac{3}{2}x + 2
\]

Would you like further details or have any questions about this solution?

### Related questions:
1. How would the equation change if the line were perpendicular instead of parallel?
2. What is the y-intercept of the new line?
3. Can you explain how to convert a line equation from point-slope form to slope-intercept form?
4. What is the general form of a linear equation?
5. How do we determine the equation of a line passing through two given points?

### Tip:
When finding equations of parallel lines, remember that they always share the same slope but have different y-intercepts unless they are the same line.

Write an equation of the line passing through the point (-4, -4) that is parallel to the line y = 3/2x - 1.

Learn how to find the equation of a line parallel to y = 3/2x - 1 passing through the point (-4, -4). This step-by-step guide covers essential algebraic concepts such as slope-intercept form and point-slope form, ideal for students in Grades 9-10.

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