Answer
Plot the y-intercept at (0, 2). Use the slope \( \frac{6}{7} \) to find another point by moving 7 units right and 6 units up to (7, 8). Draw a straight line through these points to graph the equation \( y = \frac{6}{7}x + 2 \).
Solution
Certainly! Let's graph the line given by the equation:
\[ y = \frac{6}{7}x + 2 \]
### Step 1: Identify the Y-Intercept
The equation is in the slope-intercept form \( y = mx + b \), where:
- \( m \) is the slope.
- \( b \) is the y-intercept.
For \( y = \frac{6}{7}x + 2 \):
- **Y-Intercept (\( b \))**: \( 2 \)
This means the line crosses the **y-axis** at the point **(0, 2)**.
### Step 2: Identify the Slope
- **Slope (\( m \))**: \( \frac{6}{7} \)
The slope indicates the rise over the run:
- **Rise**: 6 units (upwards)
- **Run**: 7 units (to the right)
### Step 3: Plot the Y-Intercept
Start by plotting the y-intercept on the graph:
- **Point A**: (0, 2)
### Step 4: Use the Slope to Find Another Point
From **Point A (0, 2)**:
- **Run**: Move **7 units to the right** to reach \( x = 7 \).
- **Rise**: Move **6 units up** to reach \( y = 8 \).
So, the next point is:
- **Point B**: (7, 8)
### Step 5: Draw the Line
Connect **Point A (0, 2)** and **Point B (7, 8)** with a straight line. This line extends infinitely in both directions.
### Step 6: (Optional) Plot Additional Points
For greater accuracy, you can plot more points using the slope:
- From **Point B (7, 8)**:
- **Run**: 7 units to the right → \( x = 14 \)
- **Rise**: 6 units up → \( y = 14 \)
- **Point C**: (14, 14)
Or, moving in the opposite direction:
- From **Point A (0, 2)**:
- **Run**: 7 units to the left → \( x = -7 \)
- **Rise**: 6 units down → \( y = -4 \)
- **Point D**: (-7, -4)
### Visual Representation
While I can't create an interactive graph here, here's a simple sketch of how the points align:
```
y
|
14| C (14,14)
|
8 | B (7,8)
|
2 | A (0,2)
|
-4| D (-7,-4)
|
|----------------------------- x
```
### Summary of Points to Plot:
- **(0, 2)** – Y-intercept
- **(7, 8)** – Using the slope
- **(14, 14)** – Continuing with the slope
- **(-7, -4)** – Going in the opposite direction
By plotting these points and drawing a straight line through them, you'll have an accurate graph of the equation \( y = \frac{6}{7}x + 2 \).
If you're using graphing software or an online tool, you can click on these points to place them and then draw the line accordingly.
Reviewed and approved by the UpStudy tutoring team
Explain
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