https://file.aiquickdraw.com/mathbot/file/1730382020543z5v2cl8f.jpg

To analyze the question, let’s examine the given relation:

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

The question asks to select all statements that are correct about this relation.

### Statement Analysis

1. **Statement A:** "It is in the form \( y = mx + b \)."
   - The equation \( y = -\frac{4}{5}x + \frac{1}{2} \) is indeed in the form \( y = mx + b \), where \( m = -\frac{4}{5} \) (the slope) and \( b = \frac{1}{2} \) (the y-intercept). Therefore, **Statement A is correct**.

2. **Statement B:** "It is a function."
   - This is a linear equation where for each \( x \)-value, there is exactly one \( y \)-value. This satisfies the definition of a function, so **Statement B is correct**.

3. **Statement C:** "Its graph is a straight line."
   - Linear equations in the form \( y = mx + b \) always produce a straight line when graphed. Therefore, **Statement C is correct**.

### Conclusion
All statements (A, B, and C) are correct.

Would you like a deeper explanation on any of these points or have further questions?

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Here are 5 related questions to deepen your understanding:
1. What is the slope \( m \) in the equation \( y = mx + b \)?
2. Why does the form \( y = mx + b \) represent a linear function?
3. How do we determine if an equation is a function?
4. What would change in the graph if the slope were positive instead of negative?
5. How can you identify the y-intercept directly from the equation?

**Tip:** For linear equations, the coefficient of \( x \) (the slope) determines the angle of the line, and the constant term (y-intercept) shows where the line crosses the y-axis.

Select ALL statements that are correct about the relation y = -4/5x + 1/2.

Explore the properties of the linear equation y = -4/5x + 1/2 by identifying if it meets specific criteria such as being in the slope-intercept form y = mx + b, representing a function, and producing a straight line graph. This problem reinforces knowledge of linear functions and graphing for Grades 8-10 students.

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