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The given equation is:

\[
10x - 10y = 7
\]

We need to rewrite it in **slope-intercept form**, which has the structure:

\[
y = mx + b
\]

where \(m\) is the slope and \(b\) is the y-intercept. Let’s rearrange the given equation.

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### Steps:

1. **Isolate the \(y\)-term**:
   \[
   -10y = -10x + 7
   \]
   (We subtracted \(10x\) from both sides.)

2. **Solve for \(y\)** by dividing every term by \(-10\):
   \[
   y = \frac{-10x}{-10} + \frac{7}{-10}
   \]

3. **Simplify**:
   \[
   y = x - \frac{7}{10}
   \]

---

### Final Answer:

The slope-intercept form of the equation is:

\[
y = x - \frac{7}{10}
   \quad \text{(where \(m = 1\) and \(b = -\frac{7}{10}\))}.
\]

---

Would you like more details or further clarifications?

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Here are 5 follow-up questions to extend your understanding:
1. What is the slope and what does it represent in a graph?
2. How do you graph a line using slope-intercept form?
3. What happens to the graph if you change the slope?
4. How can you convert from slope-intercept form back to standard form?
5. What are other forms of linear equations besides slope-intercept form?

**Tip:** Knowing how to manipulate equations into slope-intercept form makes it easier to graph them quickly!

Rewrite the following equation in slope-intercept form: 10x - 10y = 7.

Learn how to rewrite the linear equation 10x - 10y = 7 in slope-intercept form with a step-by-step solution. This algebra problem covers key concepts, including isolating y and simplifying terms. Ideal for students in Grades 7-10.

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