The table asks you to choose values for $x$, substitute them into the equation $y = 2x - 3$, and calculate the corresponding $y$-values. Let's fill in the table by choosing a few values for $x$ and calculating $y$.

Steps:

1. Start with a few values for $x$, such as $x = -2$, $x = 0$, and $x = 2$.
2. Substitute each $x$ into the equation $y = 2x - 3$.

Calculation:

• When $x = -2$: $y = 2(-2) - 3 = -4 - 3 = -7$ So, $y = -7$.

• When $x = 0$: $y = 2(0) - 3 = 0 - 3 = -3$ So, $y = -3$.

• When $x = 2$: $y = 2(2) - 3 = 4 - 3 = 1$ So, $y = 1$.

Completed Table:

Now, you can plot these points $(-2, -7)$, $(0, -3)$, and $(2, 1)$ on the graph. Connect the points to draw the line.

Would you like more details on how to plot these points or graph the line?

Follow-up Questions:

1. What happens to the graph if the slope (the coefficient of $x$) changes?
2. What does the $y$-intercept tell you about the graph?
3. Can you choose another value for $x$ to add more points to the table?
4. How would the equation change if it were shifted upwards by 4 units?
5. What is the effect of multiplying the entire equation by a constant?

Tip:

When choosing values for $x$, it's often helpful to pick values that are easy to calculate and cover both negative, zero, and positive numbers to get a clear graph of the line.