what is the Y intercepts of 3X plus 8Y equals 48

To find the y-intercept of the equation \( 3X + 8Y = 48 \), follow these steps:

1. The y-intercept occurs when \( X = 0 \). So, substitute \( X = 0 \) into the equation:

\[
3(0) + 8Y = 48
\]

2. Simplifying the equation:

\[
8Y = 48
\]

3. Solve for \( Y \):

\[
Y = \frac{48}{8} = 6
\]

Therefore, the y-intercept is \( Y = 6 \), or as a point, it is \( (0, 6) \).

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

Here are 5 related questions:
1. How do you find the x-intercept of a line?
2. What is the slope of the line \( 3X + 8Y = 48 \)?
3. Can you rewrite the equation \( 3X + 8Y = 48 \) in slope-intercept form?
4. What happens to the y-intercept if the equation changes to \( 3X + 8Y = 60 \)?
5. How would you graph the line \( 3X + 8Y = 48 \)?

**Tip**: The y-intercept is always the point where the graph crosses the y-axis (when \( X = 0 \)).

Discover how to find the y-intercept of the equation 3X + 8Y = 48 with a step-by-step explanation. This problem highlights key algebraic concepts, including solving linear equations and understanding intercepts. Suitable for students in Grades 7-9.

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