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We are tasked with graphing the line given by the equation:

\[
y + 3 = \frac{9}{7}(x + 2)
\]

Let’s rewrite this into **slope-intercept form** \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.

---

### Step 1: Simplify the equation
Start with:
\[
y + 3 = \frac{9}{7}(x + 2)
\]

Distribute the slope \(\frac{9}{7}\) on the right-hand side:
\[
y + 3 = \frac{9}{7}x + \frac{9}{7} \cdot 2
\]

Simplify:
\[
y + 3 = \frac{9}{7}x + \frac{18}{7}
\]

Subtract \(3\) from both sides:
\[
y = \frac{9}{7}x + \frac{18}{7} - 3
\]

Write \(3\) as a fraction with denominator \(7\): \(3 = \frac{21}{7}\):
\[
y = \frac{9}{7}x + \frac{18}{7} - \frac{21}{7}
\]

Combine like terms:
\[
y = \frac{9}{7}x - \frac{3}{7}
\]

---

### Step 2: Identify slope and y-intercept
From the simplified equation \(y = \frac{9}{7}x - \frac{3}{7}\):
- The **slope** \(m = \frac{9}{7}\),
- The **y-intercept** \(b = -\frac{3}{7}\) (approximately -0.43).

---

### Step 3: Plot the line
1. Start at the **y-intercept**: \(b = -\frac{3}{7}\) or about \(-0.43\) on the y-axis.
2. Use the slope \(m = \frac{9}{7}\) to move:
   - **Up 9 units** (rise),
   - **Right 7 units** (run).

---

### Step 4: Points on the graph
To make it easier, find a couple of exact points:
1. At \(x = 0\):  
   \[
   y = \frac{9}{7}(0) - \frac{3}{7} = -\frac{3}{7}
   \]  
   So, point \((0, -\frac{3}{7})\).

2. At \(x = 7\):  
   \[
   y = \frac{9}{7}(7) - \frac{3}{7} = 9 - \frac{3}{7} = \frac{63}{7} - \frac{3}{7} = \frac{60}{7} \approx 8.57
   \]  
   So, point \((7, 8.57)\).

3. At \(x = -7\):  
   \[
   y = \frac{9}{7}(-7) - \frac{3}{7} = -9 - \frac{3}{7} = -\frac{63}{7} - \frac{3}{7} = -\frac{66}{7} \approx -9.43
   \]  
   So, point \((-7, -9.43)\).

---

### Step 5: Plot and connect the points
- Plot \((0, -0.43)\), \((7, 8.57)\), and \((-7, -9.43)\).
- Draw a straight line through these points.

---

Would you like more details on graphing or additional explanations?

### Related Questions:
1. How do you determine the slope and y-intercept of a line from an equation?
2. What does the slope represent on a graph?
3. How can you graph a line given a point and a slope?
4. How do you find points on a line using the slope-intercept form?
5. How can you convert a point-slope equation into slope-intercept form?

### Tip:
When graphing with fractions, convert small steps into approximate decimals for easier plotting on the graph!

Graph the line given by the equation: y + 3 = (9/7)(x + 2).

Learn how to graph the line y + 3 = (9/7)(x + 2) by converting it into slope-intercept form. This problem covers slope determination, y-intercept identification, and plotting points for accurate graphing. Suitable for students in Grades 8-10.

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