Question

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

Explanation:

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

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 \( (-5,0) \)

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

If we want to rewrite the function in slope - intercept form (\( y=mx + b \), where \( m \) is the slope and \( b \) is the y - intercept):
\( g(x)=\frac{-x - 5}{3}=\frac{-x}{3}-\frac{5}{3}=- \frac{1}{3}x-\frac{5}{3} \)
The slope \( m =-\frac{1}{3} \) and the y - intercept \( b =-\frac{5}{3} \)

Answer:

The x - intercept is \( x = - 5 \) (point \( (-5,0) \)), the y - intercept is \( y=-\frac{5}{3} \) (point \( (0,-\frac{5}{3}) \)), and the function in slope - intercept form is \( g(x)=-\frac{1}{3}x-\frac{5}{3} \) with slope \( -\frac{1}{3} \) and y - intercept \( -\frac{5}{3} \)