To convert the equation from point-slope form to slope-intercept form, we'll simplify and rearrange the equation.

### Step 1: Start with the point-slope form
We have:
\[
y - 2 = \frac{2}{11}(x - 7)
\]

### Step 2: Distribute the slope
Distribute \(\frac{2}{11}\) to both terms inside the parentheses:
\[
y - 2 = \frac{2}{11}x - \frac{14}{11}
\]

### Step 3: Isolate \(y\)
Add 2 to both sides to solve for \(y\):
\[
y = \frac{2}{11}x - \frac{14}{11} + 2
\]

### Step 4: Combine the constant terms
Convert 2 to a fraction with a denominator of 11:
\[
2 = \frac{22}{11}
\]
So the equation becomes:
\[
y = \frac{2}{11}x - \frac{14}{11} + \frac{22}{11}
\]
\[
y = \frac{2}{11}x + \frac{8}{11}
\]

### Final Answer
The slope-intercept form of the equation is:
\[
y = \frac{2}{11}x + \frac{8}{11}
\]

This equation is now in the form \( y = mx + b \), where \( m = \frac{2}{11} \) is the slope, and \( b = \frac{8}{11} \) is the y-intercept.

Would you like further explanations or help with another question?

### Related Questions:
1. How do you determine the y-intercept from a graph?
2. What does the slope \( m \) represent in the context of a linear equation?
3. How would the equation change if the slope were negative?
4. How can you quickly graph a line using its slope-intercept form?
5. What are some real-world applications of linear equations in slope-intercept form?

### Tip:
When working with fractions in slope-intercept form, ensure to simplify them when possible to make the equation easier to interpret and use.

Learn how to convert a linear equation from point-slope form to slope-intercept form step-by-step. This problem covers fundamental algebraic concepts, including the calculation of slope and y-intercept. Suitable for students in Grades 7-9.

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