The graph of the function $f(x) = 3 - x$ represents a straight line because it is a linear equation in the form $f(x) = mx + b$, where:

• $m = -1$: This is the slope, indicating that the line decreases by 1 unit in $y$ for every 1 unit increase in $x$ (a negative slope means the line is slanting downward from left to right).
• $b = 3$: This is the $y$-intercept, where the line crosses the $y$-axis at $(0, 3)$.

Key Features:

1. The slope is $-1$, meaning the line tilts downward.
2. The $y$-intercept is $(0, 3)$.
3. The $x$-intercept is $(3, 0)$, found by solving $3 - x = 0$.
4. The line extends infinitely in both directions.
5. It is symmetric about no specific axis or point since the slope isn't zero or undefined.

If graphed, the line passes through $(0, 3)$ and slopes down to $(3, 0)$, forming a simple descending linear function.

Would you like a visual graph or further clarification?

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Related Questions:

1. What are the coordinates of specific points on this line?
2. How do you calculate the slope of a line from a given function?
3. What transformations would occur if the slope or intercept changed?
4. How is this function different from $f(x) = x - 3$?
5. What is the domain and range of $f(x) = 3 - x$?

Tip:

The slope tells how steeply the line rises or falls. Memorizing this helps with quick graphing!