Answer
To graph the line \( y = \frac{9}{7}x - 10 \):
1. **Plot the \( y \)-intercept** at (0, -10).
2. **Use the slope** \( \frac{9}{7} \) to find another point: move 7 units right and 9 units up from (0, -10) to (7, -1).
3. **Draw a straight line** through these points.
This line represents the equation \( y = \frac{9}{7}x - 10 \).
Solution
To graph the line \( y = \frac{9}{7}x - 10 \) using the slope and \( y \)-intercept, follow these steps:
### 1. Identify the \( y \)-Intercept
The \( y \)-intercept is the point where the line crosses the \( y \)-axis. This occurs when \( x = 0 \).
\[
y = \frac{9}{7}(0) - 10 = -10
\]
So, the \( y \)-intercept is **(0, -10)**.
### 2. Identify the Slope
The slope-intercept form of a line is:
\[
y = mx + b
\]
where:
- \( m \) is the slope
- \( b \) is the \( y \)-intercept
From your equation:
\[
m = \frac{9}{7}
\]
This means that for every increase of 7 units in \( x \), \( y \) increases by 9 units.
### 3. Plot the \( y \)-Intercept
Start by plotting the point **(0, -10)** on the coordinate plane.
### 4. Use the Slope to Find a Second Point
From the \( y \)-intercept (0, -10):
- **Rise:** Move up 9 units (since the slope is positive).
- **Run:** Move right 7 units.
So, from (0, -10):
- Move right to \( x = 7 \)
- Move up to \( y = -10 + 9 = -1 \)
This gives you the second point **(7, -1)**.
### 5. Draw the Line
Connect the two points with a straight line extending in both directions. This is the graph of the equation \( y = \frac{9}{7}x - 10 \).
### Visual Representation
While I can't provide an interactive graph here, here's a simple sketch of how the graph would look:
```
y
|
10|
|
|
|
|
|
|
|
|
0|------------------------ x
|
|
|
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|
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-10|* (0, -10)
```
- The point \((0, -10)\) is the \( y \)-intercept.
- From \((0, -10)\), move right 7 units and up 9 units to reach \((7, -1)\).
- Draw a straight line through these points.
### Summary of Points to Plot
1. **(0, -10)** — \( y \)-intercept
2. **(7, -1)** — Using the slope \( \frac{9}{7} \)
You can plot additional points using the slope if needed, but these two points are sufficient to draw the line accurately.
### Interactive Graphing Tools
For a more interactive experience, you can use online graphing tools such as:
- [Desmos](https://www.desmos.com/calculator)
- [GeoGebra](https://www.geogebra.org/graphing)
These platforms allow you to input the equation directly and visualize the graph dynamically.
Reviewed and approved by the UpStudy tutoring team
Explain
Simplify this solution
