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To find the x- and y-intercepts for the equation \(-10x + y = 35\), let's solve each intercept separately:

1. **Finding the x-intercept**:
   - The x-intercept occurs when \(y = 0\).
   - Substitute \(y = 0\) into the equation:
     \[
     -10x + 0 = 35
     \]
     \[
     -10x = 35
     \]
   - Solve for \(x\):
     \[
     x = \frac{35}{-10} = -\frac{7}{2}
     \]
   - So, the x-intercept is \(x = -\frac{7}{2}\).

2. **Finding the y-intercept**:
   - The y-intercept occurs when \(x = 0\).
   - Substitute \(x = 0\) into the equation:
     \[
     -10(0) + y = 35
     \]
     \[
     y = 35
     \]
   - So, the y-intercept is \(y = 35\).

### Final Answer
- **x-intercept**: \(-\frac{7}{2}\)
- **y-intercept**: \(35\)

Would you like more details on how I solved these steps, or do you have any questions?

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### Related Questions
1. How would you find the intercepts for a similar equation like \(5x - 3y = 15\)?
2. What do x- and y-intercepts represent on a graph?
3. Can an equation have more than one x- or y-intercept?
4. How can you rewrite an equation in slope-intercept form to make graphing easier?
5. What happens to the intercepts if we change the constant term in the equation?

#### Tip
To check intercepts quickly, remember that setting \(y = 0\) gives the x-intercept, and setting \(x = 0\) gives the y-intercept.

Find the x- and y-intercepts of the graph of -10x + y = 35. State each answer as an integer or an improper fraction in simplest form.

Learn how to find the x- and y-intercepts for the linear equation -10x + y = 35. This guide provides a step-by-step solution to find intercepts by setting variables to zero and solving for the remaining variable. Ideal for students in Grades 7-9 studying Algebra.

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