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Here's a clearer breakdown of the problems from your image:

1. **Problem 16**: If the line through points \((-2, 4)\) and \((5, d)\) is parallel to the line \(y = 3x + 4\), what is the value of \(d\)?

2. **Problem 17**: Solve the equation \(\frac{5(x + 4)}{2} + 7 = 37\) and then evaluate \(3x - 9\).

3. **Problem 18**: Solve the equation \(\frac{-8b - (-9)}{-10} = 17\).

I will now solve each of these problems step by step.

### Problem 16: Equation of the Line and Value of \(d\)

Given that the slope of the line \(y = 3x + 4\) is 3, we find the slope between the points \((-2, 4)\) and \((5, d)\). The slope formula between these points is:
\[
m = \frac{d - 4}{5 - (-2)} = \frac{d - 4}{7}
\]

Setting this equal to 3:
\[
\frac{d - 4}{7} = 3
\]

Solving for \(d\):
\[
d - 4 = 21 \implies d = 25
\]

### Problem 17: Solving the Equation

Given:
\[
\frac{5(x + 4)}{2} + 7 = 37
\]

Subtract 7 from both sides:
\[
\frac{5(x + 4)}{2} = 30
\]

Multiply both sides by 2:
\[
5(x + 4) = 60
\]

Divide both sides by 5:
\[
x + 4 = 12
\]

Subtract 4 from both sides:
\[
x = 8
\]

Now, evaluate \(3x - 9\):
\[
3(8) - 9 = 24 - 9 = 15
\]

### Problem 18: Solving for \(b\)

Given:
\[
\frac{-8b - (-9)}{-10} = 17
\]

Simplify the numerator:
\[
\frac{-8b + 9}{-10} = 17
\]

Multiply both sides by \(-10\):
\[
-8b + 9 = -170
\]

Subtract 9 from both sides:
\[
-8b = -179
\]

Divide both sides by \(-8\):
\[
b = \frac{179}{8}
\]

Simplified, \(b = 22.375\).

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If you have any questions about these solutions or need further clarification, please let me know!

### Additional Questions to Expand Your Understanding:
1. How do you determine the slope between two points on a graph?
2. What properties do parallel lines share regarding their slopes?
3. How can you solve multi-step equations that involve fractions?
4. What are the common mistakes to avoid when solving for variables in equations?
5. How can you double-check your solutions for equations?

**Tip:** Always check if your final answers make sense by substituting them back into the original equations.

If the line through (-2, 4) and (5, d) is parallel to y = 3x + 4, what is the value of d?

Determine the value of d for the line through points (-2, 4) and (5, d) to be parallel to y = 3x + 4. This problem involves concepts like slope and parallel line properties, suitable for Grade 9 students.

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