Question

give the slope and y-intercept for the graph of the function $f(x) = \frac{x}{3} - 6$.
the slope is help (fractions)
the y-intercept is help (fractions)

Explanation:

Step1: Recall the slope - intercept form

The slope - intercept form of a linear function is \(y = mx + b\), where \(m\) is the slope and \(b\) is the \(y\) - intercept.

Step2: Rewrite the given function

The given function is \(f(x)=\frac{x}{3}-6\). We can rewrite \(f(x)\) as \(y=\frac{1}{3}x-6\) (since \(y = f(x)\)).

Step3: Identify the slope and \(y\) - intercept

Comparing \(y=\frac{1}{3}x - 6\) with \(y=mx + b\):

• For the slope \(m\): We can see that \(m=\frac{1}{3}\).
• For the \(y\) - intercept \(b\): We can see that \(b=- 6\).

Answer:

The slope is \(\frac{1}{3}\)
The \(y\) - intercept is \(-6\)