Question

find the linear function with the following properties.\\( f(0) = -6 \\)\\( \text{slope of } f = -2 \\)\\( f(x) = \boxed{} \\)

Explanation:

Step1: Recall linear function form

The standard form of a linear function is $f(x) = mx + b$, where $m$ is the slope, and $b$ is the y-intercept ($f(0)$).

Step2: Assign given values

We are given slope $m = -2$, and $f(0) = b = -6$. Substitute these into the form:
$f(x) = -2x + (-6)$

Step3: Simplify the function

$f(x) = -2x - 6$

Answer:

$f(x) = -2x - 6$