The equation you provided is a **linear equation** in two variables, \( x \) and \( y \). To solve for one variable in terms of the other, we can rearrange the equation. Here’s how we can do it for \( y \):

Given:
\[
9x - 5y = 10
\]

### Solve for \( y \):
1. Start by isolating \( 5y \):
\[
9x - 10 = 5y
\]

2. Divide both sides by 5:
\[
y = \frac{9x - 10}{5}
\]

This is the equation of a straight line in slope-intercept form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.

Would you like more details or a step-by-step explanation?

Here are five related questions:
1. How do we find the slope of a linear equation?
2. What is the graph of this equation?
3. How can we solve for \( x \) instead of \( y \)?
4. What happens if you substitute a specific value for \( x \)?
5. How can you write this equation in standard form?

**Tip:** Linear equations can always be graphed as straight lines, where the slope defines the steepness.

Discover how to solve the linear equation 9x - 5y = 10 by isolating y and expressing it in slope-intercept form. This detailed explanation covers core algebra concepts, including finding the slope and y-intercept. Ideal for students in Grades 8-10.

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