Algebraically determine the x- and y-intercepts of each function. y=-3/2x+8

To determine the intercepts of the function \( y = -\frac{3}{2}x + 8 \), we need to find the **x-intercept** and the **y-intercept** algebraically.

### 1. **Y-intercept**:
The y-intercept occurs when \( x = 0 \). We substitute \( x = 0 \) into the equation and solve for \( y \).

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

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

### 2. **X-intercept**:
The x-intercept occurs when \( y = 0 \). We substitute \( y = 0 \) into the equation and solve for \( x \).

\[
0 = -\frac{3}{2}x + 8
\]
Now, solve for \( x \):
\[
\frac{3}{2}x = 8
\]
Multiply both sides by \( \frac{2}{3} \) to isolate \( x \):
\[
x = \frac{8 \times 2}{3} = \frac{16}{3}
\]

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

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

Would you like further details on any of these steps?

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Here are 5 related questions to deepen your understanding:
1. How would you find the intercepts if the slope were a positive fraction?
2. What happens to the intercepts if the constant in the equation changes?
3. How does the slope of the line affect the steepness of the graph?
4. How would the intercepts change if the equation was multiplied by 2?
5. What is the geometric significance of the x- and y-intercepts?

**Tip**: To quickly find the x-intercept of any linear equation, set \( y = 0 \) and solve for \( x \) using algebra.

Algebraically determine the x- and y-intercepts of each function. y = -3/2x + 8

Learn how to find the x- and y-intercepts of the linear function y = -3/2x + 8. This problem explains how to solve algebraically using basic principles of algebra and linear equations. Ideal for students in Grades 8-10, this solution covers intercepts and slope-intercept form.

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