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Let's analyze each problem to determine if \( y \) can be defined as a linear function of \( x \).

### Problem 4:
The equation is:
\[
-9x - 8y = 9
\]

To determine if this defines \( y \) as a linear function of \( x \), we need to solve for \( y \) in terms of \( x \).

1. **Rearrange the equation** to isolate \( y \):
   \[
   -8y = 9 + 9x
   \]

2. **Divide by \(-8\)** to solve for \( y \):
   \[
   y = -\frac{9}{8}x - \frac{9}{8}
   \]

Since the equation is now in the form \( y = mx + b \) (where \( m = -\frac{9}{8} \) and \( b = -\frac{9}{8} \)), this does define \( y \) as a linear function of \( x \). Therefore, the answer is **Yes**, and \( y = -\frac{9}{8}x - \frac{9}{8} \).

### Problem 5:
The equation is:
\[
10x = 3y + 4
\]

Again, let’s rearrange to see if we can express \( y \) in terms of \( x \).

1. **Move terms involving \( y \)** to one side:
   \[
   3y = 10x - 4
   \]

2. **Divide by 3** to solve for \( y \):
   \[
   y = \frac{10}{3}x - \frac{4}{3}
   \]

This equation is also in the form \( y = mx + b \) (where \( m = \frac{10}{3} \) and \( b = -\frac{4}{3} \)), meaning it also defines \( y \) as a linear function of \( x \). The answer here is **Yes**, and \( y = \frac{10}{3}x - \frac{4}{3} \).

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Would you like further details or have any specific questions about these steps?

### Further Practice Questions:
1. How can we identify linear equations quickly without rearranging terms?
2. What are the characteristics of a non-linear function?
3. How would the process change if the equation had a \( y^2 \) term?
4. What happens if both \( x \) and \( y \) have squared terms in an equation?
5. Can the constant term in a linear equation ever be negative?

**Tip:** When rearranging equations to find if they are linear, always aim for the form \( y = mx + b \). If you can achieve this form, it confirms the function is linear.

Determine whether the equation defines y as a linear function of x. If so, write it in the form y = mx + b.

Solve problems determining whether an equation defines y as a linear function of x and rewrite it in the slope-intercept form y = mx + b. This guide includes key algebraic concepts suitable for Grades 8-10.

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