To find the linear function $f(x) = mx + b$ with the given slope and $y$-intercept, we'll use the provided information:

Given:

• Slope $m = -\frac{17}{13}$
• $y$-intercept $b = -6$ (which means the point $(0, -6)$ is on the graph)

Form of the Linear Function:

The general form of a linear function is: $f(x) = mx + b$

Substitute the Given Values:

$f(x) = -\frac{17}{13}x - 6$

So, the linear function is: $f(x) = -\frac{17}{13}x - 6$

Would you like more details or have any questions?

Here are five related questions to further your understanding:

1. What is the slope-intercept form of a linear equation?
2. How do you determine the slope and $y$-intercept from a given equation?
3. How would the graph of this function look on the Cartesian plane?
4. Can you convert the equation to standard form $Ax + By = C$?
5. What does the slope tell us about the direction of the line?

Tip: The $y$-intercept is the value of $y$ when $x = 0$. It indicates where the line crosses the $y$-axis.