The equation $y = -x$ describes a straight line with a negative slope. Here’s a breakdown of the characteristics of this line:

1. Slope: The slope of the line is -1, which means for every unit increase in $x$, $y$ decreases by 1 unit.
2. Y-intercept: When $x = 0$, $y = 0$. Thus, the line passes through the origin (0, 0).
3. X-intercept: Since the line passes through the origin, the x-intercept is also at (0, 0).
4. Graph: The line slants downward from left to right, creating a 45-degree angle with the x-axis.
5. General behavior: The values of $y$ decrease as the values of $x$ increase.

Would you like to explore this further or have any questions?

Here are some related questions to deepen your understanding:

1. How would the line change if the equation was $y = -2x$ instead?
2. What happens to the graph of $y = -x$ if a constant, like $y = -x + 3$, is added?
3. How do you find the equation of a line that is perpendicular to $y = -x$?
4. Can you find the distance between the origin and a point on this line, say at $x = 3$?
5. How would the graph look if it were $y = x$ instead?

Tip: The coefficient of $x$ in a linear equation determines the slope of the line, indicating its steepness and direction.