Find the X and Y in intercepts of y=-3/2x+8

To find the intercepts of the equation \( y = -\frac{3}{2}x + 8 \), we'll calculate both the \( x \)-intercept and \( y \)-intercept:

### 1. **Y-intercept**:
The \( y \)-intercept occurs when \( x = 0 \). Substituting \( x = 0 \) into the equation:

\[
y = -\frac{3}{2}(0) + 8 = 8
\]

Thus, the \( y \)-intercept is \( (0, 8) \).

### 2. **X-intercept**:
The \( x \)-intercept occurs when \( y = 0 \). Setting \( y = 0 \) in the equation and solving for \( x \):

\[
0 = -\frac{3}{2}x + 8
\]

Subtract 8 from both sides:

\[
-\frac{3}{2}x = -8
\]

Multiply both sides by \( -\frac{2}{3} \) to solve for \( x \):

\[
x = \frac{16}{3}
\]

Thus, the \( x \)-intercept is \( \left( \frac{16}{3}, 0 \right) \).

### Summary:
- \( x \)-intercept: \( \left( \frac{16}{3}, 0 \right) \)
- \( y \)-intercept: \( (0, 8) \)

Would you like more details on any part of this? Here are some related questions to explore:

1. How can you use intercepts to graph a line?
2. What is the significance of the slope \( -\frac{3}{2} \) in this equation?
3. How would you write the equation in standard form?
4. What are the intercepts of other linear equations like \( y = 2x + 5 \)?
5. How does the slope-intercept form of a line help in solving real-life problems?

**Tip:** To graph a linear equation, the intercepts give you two points you can plot, making it easier to draw the entire line!

Learn how to find the X and Y intercepts for the linear equation y = -3/2x + 8. This step-by-step solution covers key algebraic concepts such as solving for intercepts and using the slope-intercept form. Suitable for students in Grades 8-10.

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