Answer
To graph the equation \( y = -3x - 1 \):
1. Plot the y-intercept at \( (0, -1) \).
2. Use the slope of -3 to find another point: move 1 unit right and 3 units down to \( (1, -4) \).
3. Draw a straight line through these points.
This line represents the equation \( y = -3x - 1 \).
Solution
Sure! Let's graph the equation \( y = -3x - 1 \) using the **slope-intercept form**, which is:
\[
y = mx + b
\]
Where:
- \( m \) is the **slope** of the line.
- \( b \) is the **y-intercept** (the point where the line crosses the y-axis).
### Step 1: Identify the Slope and Y-Intercept
For the equation \( y = -3x - 1 \):
- **Slope (\( m \))**: -3
- **Y-Intercept (\( b \))**: -1
### Step 2: Plot the Y-Intercept
Start by plotting the y-intercept on the graph.
- The y-intercept is \(-1\), so plot the point **\( (0, -1) \)** on the y-axis.
### Step 3: Use the Slope to Find Another Point
The slope \( m = -3 \) can be interpreted as:
\[
\text{Slope} = \frac{\text{Rise}}{\text{Run}} = \frac{-3}{1}
\]
This means:
- **Run (horizontal change)**: Move **1 unit to the right**.
- **Rise (vertical change)**: Move **3 units down** (since it's negative).
Starting from the y-intercept \( (0, -1) \):
- Move 1 unit to the right: \( x = 0 + 1 = 1 \).
- Move 3 units down: \( y = -1 - 3 = -4 \).
So, the second point is **\( (1, -4) \)**.
### Step 4: Plot the Second Point and Draw the Line
- Plot the second point \( (1, -4) \) on the graph.
- Draw a straight line passing through both points. This line represents the equation \( y = -3x - 1 \).
### Visual Representation
Here's a simple graph illustrating the equation:
```
y
|
5 |
4 |
3 |
2 |
1 |
0 |--------------------- x
-1|* (0, -1)
-2|
-3|
-4| * (1, -4)
-5|
-6|
```
- **Point \( (0, -1) \)** is marked with an asterisk (*) on the y-axis.
- **Point \( (1, -4) \)** is marked with an asterisk (*) in the fourth quadrant.
- The straight line passing through these points represents the equation \( y = -3x - 1 \).
### Summary
- **Y-Intercept (\( b \))**: The line crosses the y-axis at \( (0, -1) \).
- **Slope (\( m \))**: The line decreases by 3 units vertically for every 1 unit it moves to the right horizontally.
- **Direction**: Since the slope is negative, the line slopes downward from left to right.
By following these steps, you can graph any linear equation in slope-intercept form!
Answered by UpStudy AI and reviewed by a Professional Tutor
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