Question

1. $g(x)=\frac{-x - 5}{3}$

Explanation:

Since the problem seems to be about graphing the function \( g(x)=\frac{-x - 5}{3} \) or analyzing it (maybe finding intercepts, slope, etc.), let's assume we want to find the x - intercept and y - intercept to graph it.

Step - by - Step Format (Mathematics - Algebra/Calculus)

Step 1: Find the y - intercept

The y - intercept occurs when \( x = 0 \). Substitute \( x=0 \) into the function \( g(x)=\frac{-x - 5}{3} \).
\( g(0)=\frac{-0 - 5}{3}=\frac{-5}{3}\approx - 1.67 \)
So the y - intercept is at the point \( (0,-\frac{5}{3}) \).

Step 2: Find the x - intercept

The x - intercept occurs when \( g(x)=0 \). Set \( \frac{-x - 5}{3}=0 \).
Multiply both sides of the equation by 3: \( -x - 5 = 0\times3=0 \)
Add 5 to both sides: \( -x=5 \)
Multiply both sides by - 1: \( x=-5 \)
So the x - intercept is at the point \( (-5,0) \).

Step 3: Analyze the slope (optional, for graphing)

We can rewrite the function \( g(x)=\frac{-x - 5}{3} \) in slope - intercept form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y - intercept.
\( g(x)=-\frac{1}{3}x-\frac{5}{3} \). The slope \( m =-\frac{1}{3} \), which means for every 3 units we move to the right along the x - axis, we move down 1 unit along the y - axis.

To graph the line, we can plot the x - intercept \( (-5,0) \) and the y - intercept \( (0,-\frac{5}{3}) \) and then draw a straight line through these two points.

If the question was to find the intercepts:

Answer:

The x - intercept is \( x=-5 \) (at the point \( (-5,0) \)) and the y - intercept is \( y =-\frac{5}{3} \) (at the point \( (0,-\frac{5}{3}) \)).

If the question was to graph the function, the key points for graphing are the x - intercept \( (-5,0) \) and the y - intercept \( (0,-\frac{5}{3}) \), and the line has a slope of \( -\frac{1}{3} \).