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The problem asks which of the following is *not* true about the graph of the given equation:

\[
-\frac{2}{5}x + \frac{1}{10}y = -\frac{4}{5}
\]

Let's begin by simplifying this equation to the slope-intercept form (\(y = mx + b\)):

1. Multiply both sides of the equation by 10 to eliminate the fractions:

\[
-4x + y = -8
\]

2. Solve for \(y\):

\[
y = 4x - 8
\]

Now the equation is \(y = 4x - 8\), where:
- The slope (\(m\)) is 4.
- The \(y\)-intercept is \(-8\).

### Now, let's analyze each statement:

**A: "The \(x\)-intercept is 2 and the \(y\)-intercept is \(-8\)."**
- To find the \(x\)-intercept, set \(y = 0\) and solve for \(x\):

\[
0 = 4x - 8 \implies 4x = 8 \implies x = 2
\]

- The \(x\)-intercept is indeed 2, and we already found that the \(y\)-intercept is \(-8\), so **this statement is true**.

**B: "The function is decreasing when \(x < 2\) and increasing when \(x > 2\)."**
- The slope of the line is positive (\(m = 4\)), so the function is increasing everywhere, not decreasing at any point. **This statement is false**.

**C: "The graph passes through (1, -4) and (5, 12)."**
- Let's check these points by substituting them into the equation \(y = 4x - 8\):
  - For \((1, -4)\): \(y = 4(1) - 8 = -4\) → True.
  - For \((5, 12)\): \(y = 4(5) - 8 = 12\) → True.
  
Both points are on the graph, so **this statement is true**.

**D: "As \(x \to -\infty\), \(y \to -\infty\), and as \(x \to +\infty\), \(y \to +\infty\)."**
- Since the slope is positive, as \(x\) increases, \(y\) increases, and as \(x\) decreases, \(y\) decreases. So, **this statement is true**.

### Conclusion:
The false statement is **B**, meaning the function is not decreasing for \(x < 2\).

---

Would you like further clarification on this? Here are some related questions:

1. How do you find the slope of a linear equation?
2. How can you determine if a function is increasing or decreasing?
3. What are the differences between slope-intercept form and standard form of a line?
4. How can you determine intercepts from an equation?
5. What are the implications of a positive vs negative slope?

**Tip:** A positive slope indicates that a function is increasing, while a negative slope indicates it's decreasing.

Which of the following is not true about the graph of the equation: -2/5 x + 1/10 y = -4/5?

Explore the linear equation -2/5x + 1/10y = -4/5 and analyze its graph. Find out which statements about its intercepts, slope behavior, and specific points are true or false. This exercise is suitable for high school students, focusing on graphing, slope, and intercepts.

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