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

1. Identify the slope and y-intercept:

   • The slope ($m$) is $-2$, which means for every 1 unit increase in $x$, $y$ decreases by 2 units.
   • The y-intercept ($b$) is $3$, which means the line crosses the y-axis at the point $(0, 3)$.

2. Plot the y-intercept:

   • Start by plotting the point $(0, 3)$ on the graph.

3. Use the slope to find another point:

   • From the y-intercept $(0, 3)$, move 1 unit to the right (increase $x$ by 1) and 2 units down (since the slope is $-2$), landing at the point $(1, 1)$.
   • Plot this point $(1, 1)$ on the graph.

4. Draw the line:

   • Draw a straight line through the points $(0, 3)$ and $(1, 1)$. This line is the graph of the equation $y = -2x + 3$.

Would you like a detailed image of the graph?

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Here are 5 relative questions to consider:

1. How would the graph change if the slope was positive?
2. What happens to the graph if the y-intercept changes to -3?
3. How would you graph $y = 2x + 3$, and how does it differ from $y = -2x + 3$?
4. How can you determine the x-intercept of the line $y = -2x + 3$?
5. How would the graph look if the equation were $y = -2x$ (no y-intercept)?

Tip: When graphing, always start with the y-intercept and use the slope to find other points on the line for accuracy.