The task is to graph the linear equation $y = 3x - 5$ and fill in the table of values for $x$ and $y$.

Step-by-Step Solution:

1. Select values of $x$: To graph the equation, let's select a few values for $x$, calculate the corresponding $y$-values using the equation, and then plot these points on the graph.

   Let's choose $x = -2, 0, 2$.

2. Calculate $y$-values: Using the equation $y = 3x - 5$:

   • When $x = -2$, $y = 3(-2) - 5 = -6 - 5 = -11$
   • When $x = 0$, $y = 3(0) - 5 = -5$
   • When $x = 2$, $y = 3(2) - 5 = 6 - 5 = 1$

3. Table of values:

   $x$	$y$
   -2	-11
   0	-5
   2	1

4. Plot the points: Now, plot the points $(-2, -11)$, $(0, -5)$, and $(2, 1)$ on the graph. After plotting, draw a straight line through these points to represent the equation $y = 3x - 5$.

Would you like more details on how to draw the graph, or do you have any questions?

Here are 5 related questions to expand your understanding:

1. What is the slope of the line in the equation $y = 3x - 5$?
2. How would the graph change if the equation were $y = 3x + 5$ instead?
3. What is the y-intercept of the line $y = 3x - 5$, and how do you find it?
4. Can you explain how the slope influences the steepness of the line?
5. How would you graph $y = -3x + 5$ on the same set of axes?

Tip: When graphing linear equations, picking $x$-values near the y-intercept often gives clearer and more accurate plots!