To graph the equation $y = 2x - 3$, follow these steps:

1. Identify the slope and y-intercept:

   • The equation is in the slope-intercept form $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.
   • Here, the slope $m = 2$ and the y-intercept $b = -3$.

2. Plot the y-intercept:

   • Start by plotting the point where the line crosses the y-axis. This occurs at $(0, -3)$.

3. Use the slope to find another point:

   • The slope $2$ means that for every 1 unit you move to the right (positive direction along the x-axis), you move 2 units up (positive direction along the y-axis).
   • Starting from $(0, -3)$, move 1 unit to the right to $(1, -3)$, and then 2 units up to $(1, -1)$. Plot this point at $(1, -1)$.

4. Draw the line:

   • Connect the two points $(0, -3)$ and $(1, -1)$ with a straight line.
   • Extend the line in both directions.

5. Label the graph:

   • Make sure to label the x-axis and y-axis and write the equation $y = 2x - 3$ on the graph.

This is what the graph should look like:

• A line that crosses the y-axis at $(0, -3)$ and moves upward with a slope of 2.

Would you like me to generate a visual graph of this line?

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Here are 5 related questions:

1. How would the graph change if the slope were $\frac{1}{2}$ instead of 2?
2. What would happen to the graph if the y-intercept were $+3$ instead of $-3$?
3. How do you find the x-intercept of the line $y = 2x - 3$?
4. What is the significance of the slope in a linear equation?
5. How would you graph the line if the equation were $y = -2x + 3$?

Tip: Understanding the slope-intercept form of a linear equation can help you quickly graph any linear equation.