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Let's go through the questions one by one:

### 11a. Write an equation that is parallel to the line using \( b = -7 \).

- From the graph, it looks like the line has a slope \( m \). The equation of a line parallel to another has the same slope \( m \), so the line we write will have the same slope but may have a different \( y \)-intercept.

Given that \( b = -7 \), the equation of a parallel line could be written in the slope-intercept form:
\[
y = mx - 7
\]
where \( m \) is the slope of the line in the graph. We would need the slope from the graph to finalize this equation.

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### 11b. Write the equation of the perpendicular bisector of line AB.

To write the equation of the perpendicular bisector:
1. **Find the midpoint** of line \( AB \). The coordinates of point \( A \) and \( B \) can be obtained from the graph.
2. **Find the slope of line AB** using the formula for slope:
   \[
   m_{AB} = \frac{y_B - y_A}{x_B - x_A}
   \]
3. The slope of the perpendicular bisector is the **negative reciprocal** of the slope of line \( AB \). So if \( m_{AB} \) is the slope of line \( AB \), the slope of the perpendicular bisector is:
   \[
   m_{\perp} = -\frac{1}{m_{AB}}
   \]
4. Use the midpoint and the new slope to write the equation in point-slope form:
   \[
   y - y_1 = m_{\perp}(x - x_1)
   \]
   where \( (x_1, y_1) \) is the midpoint of \( AB \).

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### 12. If H is the midpoint of \( GI \), find \( GH \).

Given the equations for \( G \) and \( I \) are \( 5x + 2 \) and \( 9x - 10 \), respectively, the midpoint \( H \) satisfies:
\[
H = \frac{G + I}{2}
\]
Given that \( H \) is the midpoint, we can solve the equation to find \( GH \). You calculated \( GH = 17 \), which suggests this was solved correctly.

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Do you want further explanations or clarifications on these solutions?

Here are 5 additional related questions to deepen your understanding:
1. What is the general formula for a line parallel to a given line?
2. How do you find the midpoint of any line segment using two points?
3. Why is the perpendicular slope the negative reciprocal of the original slope?
4. Can you derive the equation of a line given the midpoint and slope alone?
5. How can you verify that two lines are perpendicular using their slopes?

**Tip**: When writing the equation of the perpendicular bisector, always remember to calculate the midpoint first—it serves as a key point in the equation.

Use the graph for the following questions: (a) Write an equation that is parallel to the line using b = -7, (b) Write the equation of the perpendicular bisector of line AB, (12) If H is the midpoint of GI, find GH.

Learn how to write the equation of a line parallel to another using b = -7, calculate the equation of the perpendicular bisector of line AB, and solve for GH given that H is the midpoint of line segment GI. This problem covers key concepts in coordinate geometry and slope calculations.

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