Find the Rate of Change: Analyzing y = -6x Linear Function

To solve this problem, let's follow these steps:

• Step 1: Identify the form of the given function
• Step 2: Compare the equation with the standard slope-intercept form
• Step 3: Extract the value of the slope from the equation

Now, let's work through each step:

Step 1: The given linear function is $y = -6x$. This is presented in the form $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

Step 2: Comparing $y = -6x$ with $y = mx + b$, we see that the equation lacks a constant term, indicating $b = 0$. The slope $m$ is the coefficient of $x$.

Step 3: The coefficient of $x$ is $-6$, so the slope $m$ is $-6$. Thus, the rate of change of the function is $-6$.

Therefore, the solution to the problem is $m = -6$.