The function given is:

\[ f(x) = -6x + 3 \]

This is a linear function, where:

- The slope (or gradient) \( m \) is \(-6\).
- The y-intercept (the point where the line crosses the y-axis) is \( 3 \).

### Properties:
1. **Slope**: The slope of \(-6\) indicates that for every unit increase in \( x \), \( f(x) \) decreases by 6 units.
2. **Y-intercept**: The y-intercept is 3, meaning the line crosses the y-axis at the point (0, 3).

### Graph of the Function:
The graph of this function is a straight line that slants downwards (since the slope is negative) and passes through the point (0, 3).

Would you like to see the graph of this function or need further details?

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Here are 5 related questions:

1. What is the x-intercept of the function \( f(x) = -6x + 3 \)?
2. How would you find the value of \( x \) when \( f(x) = 0 \)?
3. What is the effect of changing the slope from \(-6\) to \(-2\)?
4. How does the y-intercept change if the equation becomes \( f(x) = -6x + 7 \)?
5. How do you interpret the slope and y-intercept in a real-world context?

**Tip:** The slope of a line indicates the rate of change of the dependent variable (y) with respect to the independent variable (x).

Explore the linear function f(x) = -6x + 3. This problem involves key algebraic concepts such as slope, y-intercept, and graphing linear functions. Suitable for students in Grades 7-8.

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