The equation given is $y = -x + 3$, which is a linear equation in slope-intercept form, $y = mx + b$, where:

• $m = -1$ (the slope)
• $b = 3$ (the y-intercept).

To plot this:

1. Y-intercept: The line crosses the y-axis at $(0, 3)$.
2. Slope: The slope of -1 means for every 1 unit increase in $x$, $y$ decreases by 1. This gives a downward-sloping line from left to right.

Key points to plot:

• Start with the point $(0, 3)$.
• From $(0, 3)$, move 1 unit to the right to $x = 1$ and 1 unit down, arriving at $(1, 2)$.
• You can continue this process, moving points down and to the right, or alternatively move up and to the left to plot more points like $(-1, 4)$.

Graph description:

The line will pass through points such as:

• $(0, 3)$
• $(1, 2)$
• $(2, 1)$
• $(-1, 4)$ It slopes downwards with a slope of -1, representing a consistent decline as $x$ increases.

Would you like a detailed step-by-step solution for how to plot linear equations like this? Also, here are some related questions to expand your understanding:

1. What does the slope of a line represent in general?
2. How does changing the y-intercept affect the position of a line on a graph?
3. What happens if the slope is positive instead of negative?
4. How would the graph change if the equation were $y = -2x + 3$?
5. Can you derive the slope-intercept form from a standard form equation, $Ax + By = C$?

Tip: For linear equations, always identify the slope and intercept to quickly understand how the line behaves and where it crosses the axes.