Here's the graph of the equation $y = 1 - 2x$. The line has a negative slope of -2, indicating that it decreases as $x$ increases, and it intersects the y-axis at $(0, 1)$.

Would you like any further details or have any questions? Here are some related questions:

1. How do you determine the slope and y-intercept from the equation?
2. What is the significance of the slope and y-intercept in real-world problems?
3. How do you find the x-intercept of this line?
4. Can you graph multiple linear equations on the same plot?
5. How would this graph change if the equation were $y = 1 + 2x$?

Tip: The slope of a line indicates the rate of change; a negative slope means the line falls as you move to the right.