To graph the equation $y = -3x - 1$, we can create a table of values by selecting a few values for $x$, calculating the corresponding $y$-values, and then plotting the points on the coordinate plane.

Step-by-Step:

1. Select values for $x$: Choose values that are easy to calculate. For this example, let's use $x = -2$, $x = -1$, $x = 2$, and $x = 3$.

2. Calculate corresponding $y$-values: Substitute each $x$-value into the equation $y = -3x - 1$.

$x$	Calculation for $y$	$y$-value
$-2$	$y = -3(-2) - 1 = 6 - 1$	$y = 5$
$-1$	$y = -3(-1) - 1 = 3 - 1$	$y = 2$
$2$	$y = -3(2) - 1 = -6 - 1$	$y = -7$
$3$	$y = -3(3) - 1 = -9 - 1$	$y = -10$

Now we have the following points: $(-2, 5), (-1, 2), (2, -7), (3, -10)$

Table of Values:

$x$	$y$
-2	5
-1	2
2	-7
3	-10

Graph:

Plot these points on the graph and draw a straight line through them, as the equation represents a linear function.

Would you like a graph for this, or have any questions?

5 Follow-up Questions:

1. How does the slope of the line affect the steepness of the graph?
2. What happens to the graph if we change the slope to a positive value?
3. How would you find the intercepts of this line?
4. Can you explain how to determine the slope from the equation $y = -3x - 1$?
5. What would the graph look like if the equation were $y = -3x + 1$?

Tip:

When graphing lines, always try to choose both positive and negative values for $x$ to get a clearer picture of the line's behavior!