To find the equation of line $t$, we follow these steps:

1. Identify the slope of line $s$: The equation of line $s$ is given as: $y = -\frac{4}{3}x - 5$ The slope ($m$) of line $s$ is $-\frac{4}{3}$.

   Since line $t$ is parallel to line $s$, its slope will also be $-\frac{4}{3}$.

2. Use the point-slope form of the line equation: The point-slope form is: $y - y_1 = m(x - x_1)$ where $(x_1, y_1)$ is a point on the line, and $m$ is the slope.

   For line $t$, the given point is $(-3, 3)$ and the slope is $-\frac{4}{3}$.

   Substituting these values into the point-slope form: $y - 3 = -\frac{4}{3}(x - (-3))$ $y - 3 = -\frac{4}{3}(x + 3)$

3. Simplify the equation: Expand the right-hand side: $y - 3 = -\frac{4}{3}x - 4$ Add 3 to both sides to isolate $y$: $y = -\frac{4}{3}x - 1$

   So, the equation of line $t$ is: $y = -\frac{4}{3}x - 1$

Final Answer:

The equation of line $t$ is: $y = -\frac{4}{3}x - 1$

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Do you want me to explain any step in more detail? Here are 5 related questions for practice:

1. What would be the equation of a line perpendicular to line $s$ passing through $(-3, 3)$?
2. How do you find the slope of a line given two points on it?
3. What is the general form of the equation of a line, and how is it related to the slope-intercept form?
4. If line $t$ were vertical, what would its equation be?
5. How do you determine the distance between two parallel lines?

Tip: When working with parallel lines, remember that their slopes are always equal!