
Find the y-intercept of the given linear equation. 7x - 2y = -10.

To find the y-intercept of the linear equation \( 7x - 2y = -10 \), we need to express the equation in slope-intercept form, which is \( y = mx + b \), where \( b \) represents the y-intercept.

### Steps:

1. Start with the given equation:
   \[
   7x - 2y = -10
   \]

2. Solve for \( y \):
   - Subtract \( 7x \) from both sides:
     \[
     -2y = -7x - 10
     \]
   - Divide through by \( -2 \) to isolate \( y \):
     \[
     y = \frac{-7x - 10}{-2}
     \]
     Simplifying the right-hand side:
     \[
     y = \frac{7}{2}x + 5
     \]

3. The equation is now in the form \( y = \frac{7}{2}x + 5 \). The y-intercept is the constant term, which is \( b = 5 \).

### Conclusion:
The y-intercept is \( 5 \), meaning the line crosses the y-axis at the point \( (0, 5) \).

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Would you like more details on this process or have any further questions?

Here are 5 related questions:
1. How do you find the x-intercept of the same equation?
2. What is the slope of this line?
3. Can you graph this line based on the y-intercept and slope?
4. How do you find the intercepts of non-linear equations?
5. What is the general form of a linear equation?

**Tip**: To quickly find the y-intercept, set \( x = 0 \) in the equation!

Find the y-intercept of the given linear equation. 7x - 2y = -10.

Learn how to find the y-intercept of the linear equation 7x - 2y = -10 with a clear step-by-step solution. This algebraic problem involves rearranging the equation into slope-intercept form (y = mx + b) and solving for the y-intercept. Ideal for students in Grades 8-10.

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