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The question asks us to determine which of the following two equations represents a line that passes through the points \((-10, -7)\) and \((5, -2)\).

### Equations provided:
1. \( 3x - 5y = 20 \)
2. \( y = \frac{3}{5}x - 5 \)

### Step-by-Step Process:
We'll check both equations by determining if they satisfy the given points \((-10, -7)\) and \((5, -2)\).

#### I. Equation: \( 3x - 5y = 20 \)

1. **Substitute** the point \((-10, -7)\):
   \[
   3(-10) - 5(-7) = -30 + 35 = 5 \quad (\text{not equal to } 20)
   \]
   So, \((-10, -7)\) **does not satisfy** the first equation.

2. **Substitute** the point \((5, -2)\):
   \[
   3(5) - 5(-2) = 15 + 10 = 25 \quad (\text{not equal to } 20)
   \]
   So, \((5, -2)\) **does not satisfy** the first equation either.

Since neither point satisfies the first equation, **Equation I is not valid**.

#### II. Equation: \( y = \frac{3}{5}x - 5 \)

1. **Substitute** the point \((-10, -7)\):
   \[
   y = \frac{3}{5}(-10) - 5 = -6 - 5 = -11 \quad (\text{not equal to } -7)
   \]
   So, \((-10, -7)\) **does not satisfy** the second equation.

2. **Substitute** the point \((5, -2)\):
   \[
   y = \frac{3}{5}(5) - 5 = 3 - 5 = -2 \quad (\text{correct!})
   \]
   So, \((5, -2)\) **satisfies** the second equation.

Since only one point satisfies the second equation, **Equation II is also not valid**.

### Conclusion:
Neither of the equations satisfies both points, so the correct answer is:
\[
\boxed{\text{Neither}}
\]

Would you like more details or have any other questions?

Here are 5 related questions you might find helpful:
1. How do you derive the equation of a line from two points?
2. What is the slope-intercept form of a line?
3. How can you convert between standard form and slope-intercept form of a line?
4. How do you check if a point lies on a given line?
5. What is the significance of slope in the equation of a line?

**Tip:** Always double-check both points when testing a line equation to ensure they satisfy it completely.

Which of the following equations represents a line that passes through the points (-10, -7) and (5, -2)?

Learn how to determine whether the points (-10, -7) and (5, -2) lie on the lines represented by the equations 3x - 5y = 20 and y = (3/5)x - 5. This problem covers key concepts of linear algebra, including standard and slope-intercept forms of equations. Suitable for students in Grades 8-10.

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