A linear function has the general form:

$f(x) = mx + b$

where $m$ is the slope and $b$ is the y-intercept.

Step 1: Find the Slope

The slope $m$ is given by:

$m = \frac{f(x_2) - f(x_1)}{x_2 - x_1}$

Substituting the given points $(-10, 4)$ and $(-2, 4)$:

$m = \frac{4 - 4}{-2 - (-10)} = \frac{0}{8} = 0$

Since the slope is 0, the function is a constant function:

$f(x) = 4$

Conclusion:

The linear function satisfying the given conditions is:

$f(x) = 4$

This means that for any value of $x$, the function always outputs 4.

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Would you like additional details or an explanation of any step?

Related Questions:

1. What is the general form of a linear function with any two given points?
2. How can you determine if a function is constant just by looking at given values?
3. What does a constant function graph look like?
4. How does a horizontal line differ from a vertical line in terms of equations?
5. Can a linear function ever have an undefined slope?

Tip: A function with a slope of 0 is always a horizontal line! 🚀