Here are the graphs for the equations $y = 2x$ and $y = 2x - 3$ for $x$ values ranging from -5 to 5.

• The blue line represents $y = 2x$.
• The red line represents $y = 2x - 3$.

The graph of $y = 2x - 3$ is obtained by shifting the graph of $y = 2x$ downward by 3 units. This transformation is a vertical translation.

Would you like further details or have any questions?

Here are some related questions:

1. How would the graph change if the equation were $y = 2x + 3$?
2. What effect does multiplying $x$ by a constant (e.g., $y = 3x$) have on the graph?
3. How does the graph of $y = -2x$ compare with $y = 2x$?
4. What would happen if we added a horizontal shift, like $y = 2(x - 1)$?
5. How does changing the slope (coefficient of $x$) affect the steepness of the graph?

Tip: In transformations, vertical shifts change the $y$-intercept, while horizontal shifts change where the line crosses the $x$-axis.