To find the equation of a linear function given the slope and y-intercept, we can use the slope-intercept form of a line:

$f(x) = mx + b$

where:

• $m$ is the slope of the line,
• $b$ is the y-intercept of the line.

From the problem:

• The slope $m$ is $-\frac{3}{2}$.
• The y-intercept $b$ is $-1$.

Substituting these values into the equation:

$f(x) = -\frac{3}{2}x - 1$

So, the equation for the function is:

$f(x) = -\frac{3}{2}x - 1$

Would you like further explanation, or do you have any questions?

Here are some related questions that build on this topic:

1. How would you find the equation of a line given two points instead of a slope and y-intercept?
2. What does the slope of a line indicate about its steepness and direction?
3. How does changing the y-intercept affect the graph of a linear function?
4. Can you find the x-intercept of the function $f(x) = -\frac{3}{2}x - 1$?
5. What are the characteristics of a line with a positive slope vs. a negative slope?

Tip: Remember, the y-intercept is the point where the line crosses the y-axis, and it always occurs when $x = 0$.