Answer
To graph the line with a slope of \( -\frac{3}{10} \) passing through \( (0, -5) \), plot the y-intercept at \( (0, -5) \) and another point using the slope, such as \( (10, -8) \). Draw a straight line through these points to complete the graph.
Solution
To graph the line with a slope of \( -\frac{3}{10} \) that passes through the point \( (0, -5) \), follow these steps:
### 1. Understand the Components
- **Slope (\( m \))**: \( -\frac{3}{10} \)
- **Y-intercept (\( b \))**: \( -5 \) (since the line passes through \( (0, -5) \))
So, the equation of the line in slope-intercept form is:
\[ y = -\frac{3}{10}x - 5 \]
### 2. Plot the Y-intercept
Start by plotting the y-intercept on the graph:
- **Point**: \( (0, -5) \)
### 3. Use the Slope to Find Another Point
The slope \( \frac{\Delta y}{\Delta x} = -\frac{3}{10} \) means that for every 10 units you move to the right (positive direction on the x-axis), you move 3 units down (negative direction on the y-axis).
- **Starting Point**: \( (0, -5) \)
- **Move Right (Δx)**: \( +10 \)
- **Move Down (Δy)**: \( -3 \)
- **New Point**: \( (0 + 10, -5 - 3) = (10, -8) \)
Plot this second point:
- **Point**: \( (10, -8) \)
### 4. Draw the Line
Connect the two points with a straight line. This line represents all the solutions to the equation \( y = -\frac{3}{10}x - 5 \).
### Summary of Points
- **Y-intercept**: \( (0, -5) \)
- **Second Point**: \( (10, -8) \)
### Additional Points (Optional)
For greater accuracy, you can plot more points using the equation:
1. Let \( x = -10 \):
\[ y = -\frac{3}{10}(-10) - 5 = 3 - 5 = -2 \]
- **Point**: \( (-10, -2) \)
2. Let \( x = 20 \):
\[ y = -\frac{3}{10}(20) - 5 = -6 - 5 = -11 \]
- **Point**: \( (20, -11) \)
Plotting additional points ensures the line is accurate.
### Visual Representation
If you have graph paper or a graphing tool, you can plot the points mentioned above and draw the line accordingly. Here's a simple representation:
```
y
|
10 |
9 |
8 |
7 |
6 |
5 |
4 |
3 |
2 |
1 |
0 |--------•------------
-10 -5 0 5 10 15 20 x
(0,-5) (10,-8)
```
- The bullet points (•) represent the plotted points.
- Draw a straight line through these points extending in both directions.
### Conclusion
By following the steps above, you've successfully graphed the line with a slope of \( -\frac{3}{10} \) that passes through \( (0, -5) \). This line decreases as it moves from left to right, consistent with its negative slope.
Reviewed and approved by the UpStudy tutoring team
Explain
Simplify this solution
