The equation 5𝑥 − 8𝑦 = 20 expresses a linear relationship between 𝑥 and 𝑦.
Determine if the point (15; 7) is either on the graph of this line, above it, or below
it. Explain your thinking.

To determine if the point \((15, 7)\) is on, above, or below the graph of the line represented by the equation \(5x - 8y = 20\), we can follow these steps:

### 1. Substitute the coordinates into the equation:
Given \(x = 15\) and \(y = 7\), substitute these values into the equation:
\[
5(15) - 8(7)
\]

### 2. Calculate the left-hand side:
\[
5(15) = 75
\]
\[
8(7) = 56
\]
\[
75 - 56 = 19
\]

### 3. Compare with the right-hand side of the equation:
The equation is \(5x - 8y = 20\). After substituting \(x = 15\) and \(y = 7\), we got \(19\) on the left-hand side. The right-hand side of the equation is \(20\).

### 4. Interpretation:
- If the left-hand side equals the right-hand side (\(19 = 20\)), the point would lie **on the line**.
- If the left-hand side is less than the right-hand side (\(19 < 20\)), the point lies **below the line**.
- If the left-hand side is greater than the right-hand side (\(19 > 20\)), the point lies **above the line**.

In this case, \(19 < 20\), so the point \((15, 7)\) is **below the line**.

### Conclusion:
The point \((15, 7)\) is below the graph of the line given by the equation \(5x - 8y = 20\).

---

Would you like more details or have any questions?

Here are 8 follow-up questions to deepen your understanding:

1. How would the result change if the point was \((15, 8)\)?
2. What is the slope of the line given by the equation \(5x - 8y = 20\)?
3. How do you find the y-intercept of the line \(5x - 8y = 20\)?
4. How can you rewrite the equation \(5x - 8y = 20\) in slope-intercept form?
5. If the point \((x, y)\) lies on the line, what relationship between \(x\) and \(y\) must hold?
6. Can you find another point that lies on the line \(5x - 8y = 20\)?
7. How do you determine if a point is above or below a curve for non-linear equations?
8. What are the implications of the line's slope being positive or negative?

**Tip:** Always substitute the point's coordinates into the equation to verify its location relative to the graph.

Understand the position of point (15, 7) relative to the line represented by the equation 5x - 8y = 20. Learn how to determine if a point lies on, above, or below a linear equation through step-by-step analysis. Suitable for Grades 7-9 students.

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