The equation you provided is $Y = -x + 3$, which represents a straight line in the slope-intercept form $Y = mx + b$, where:

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

Key Details:

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

Graphing:

• When $x = 0$, $Y = 3$.
• When $x = 1$, $Y = -1 + 3 = 2$.
• When $x = -1$, $Y = 1 + 3 = 4$.

If you plot these points, the line would slope downwards from left to right due to the negative slope.

Would you like more details or have any questions?

Here are 5 related questions for deeper understanding:

1. What is the x-intercept of this line?
2. How would the graph look if the slope were positive instead?
3. What happens to the line if the y-intercept changes?
4. Can you calculate the equation of a line parallel to this one but passing through a different point?
5. How do you find the distance between this line and a point not on the line?

Tip: For any linear equation in slope-intercept form, the slope tells you the steepness and direction of the line.