Question

watch the video and then solve the problem given below.
click here to watch the video.
graph the given functions, f and g, in the same rectangular coordinate system. describe how the graph of g is related to the graph of f.
\\( f(x) = - 4x \\)
\\( g(x) = - 4x - 4 \\)
use the graphing tool to graph the functions
click to enlarge graph

Explanation:

Step1: Identify slope-intercept form

Both functions are in $y=mx+b$ form, where $m$ is slope, $b$ is y-intercept.
For $f(x)=-4x$: $m=-4$, $b=0$
For $g(x)=-4x-4$: $m=-4$, $b=-4$

Step2: Graph $f(x)$

Plot y-intercept $(0,0)$. Use slope $\frac{-4}{1}$: from $(0,0)$, move 1 right, 4 down to $(1,-4)$, draw line through points.

Step3: Graph $g(x)$

Plot y-intercept $(0,-4)$. Use slope $\frac{-4}{1}$: from $(0,-4)$, move 1 right, 4 down to $(1,-8)$, draw line through points.

Step4: Relate the two graphs

Same slope means lines are parallel. $g(x)$ has y-intercept 4 units lower than $f(x)$.

Answer:

The graph of $g(x)$ is the graph of $f(x)$ shifted 4 units downward, and the two lines are parallel (same slope, different y-intercepts).
To graph:

1. $f(x) = -4x$: passes through $(0,0)$ and $(1,-4)$
2. $g(x) = -4x-4$: passes through $(0,-4)$ and $(1,-8)$