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.