To graph the function \( g(x) = -3x - 5 \), let's analyze its components:

### 1. Identify the slope and y-intercept:

The function \( g(x) = -3x - 5 \) is a linear equation of the form \( y = mx + b \), where:

- \( m = -3 \) is the slope.
- \( b = -5 \) is the y-intercept.

### 2. Plot the y-intercept:

The y-intercept is the point where the line crosses the y-axis. This occurs when \( x = 0 \).

\[
g(0) = -3(0) - 5 = -5
\]

So, the y-intercept is at \( (0, -5) \).

### 3. Use the slope to find another point:

The slope \( m = -3 \) indicates that for every increase of 1 unit in \( x \), \( y \) decreases by 3 units.

Starting from the y-intercept \( (0, -5) \), we can move:

- 1 unit to the right (increase \( x \) by 1)
- 3 units down (decrease \( y \) by 3)

This gives us a second point at \( (1, -8) \).

### 4. Draw the line:

Plot the two points \( (0, -5) \) and \( (1, -8) \) on the coordinate plane and draw a straight line through them. Since it's a linear function, the line will continue infinitely in both directions.

### Graph Representation:

Here’s a summary of the steps to graph the function \( g(x) = -3x - 5 \):

1. Plot the y-intercept at \( (0, -5) \).
2. From \( (0, -5) \), use the slope to find another point \( (1, -8) \).
3. Draw a line through these two points.

If you have graph paper or a graphing tool, you can visualize this graph accurately.

Would you like me to provide a more detailed explanation or answer any specific questions? 

### Related Questions:

1. How does changing the slope affect the graph of a linear function?
2. What happens to the graph of \( g(x) = -3x - 5 \) if the slope is positive instead?
3. How would the graph of \( g(x) = -3x - 5 \) look if it was transformed vertically or horizontally?
4. Can you explain how to find the x-intercept of \( g(x) = -3x - 5 \)?
5. How do you graph a linear function if the equation is given in a different form, such as \( ax + by = c \)?

### Tip:

When graphing linear functions, always start by identifying the slope and y-intercept, as they provide the quickest way to plot the line.

Learn how to graph the linear function g(x) = -3x - 5 with a detailed step-by-step guide. Understand the concepts of slope, y-intercept, and plotting points. Suitable for students in Grades 7-9.

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