The given equation of line $s$ is:

$y = -\frac{4}{3}x - \frac{5}{3}$

We are told that line $t$ is parallel to line $s$, which means that the slopes of both lines are the same. The slope of line $s$ is $-\frac{4}{3}$, so the slope of line $t$ is also $-\frac{4}{3}$.

Now, we are given that line $t$ passes through the point $(-3, 3)$. To find the equation of line $t$, we can use the point-slope form of the equation of a line, which is:

$y - y_1 = m(x - x_1)$

where $m$ is the slope, and $(x_1, y_1)$ is the point the line passes through. Substituting the known values:

$y - 3 = -\frac{4}{3}(x + 3)$

Now, we will simplify this equation step by step:

1. Distribute the slope $-\frac{4}{3}$ on the right-hand side:

$y - 3 = -\frac{4}{3}x - 4$

2. Add 3 to both sides to isolate $y$:

$y = -\frac{4}{3}x - 4 + 3$

3. Simplify the constants:

$y = -\frac{4}{3}x - 1$

Thus, the equation of line $t$ in slope-intercept form is:

$y = -\frac{4}{3}x - 1$

Would you like more details or have any questions?

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Here are 5 related questions to expand on this concept:

1. How would you find the equation of a line perpendicular to line $s$?
2. How does the slope of a line relate to its steepness and direction?
3. Can you explain how to derive the slope-intercept form from the general equation of a line?
4. What is the significance of parallel and perpendicular lines in geometry?
5. How would you graph the lines $s$ and $t$ on a coordinate plane?

Tip: When two lines are parallel, their slopes are always equal.