https://file.aiquickdraw.com/mathbot/file/1725401111227vkka0a1a.jpg

To determine whether the point \((1, 3)\) lies on, above, or below the line described by the equation \(3x - 4y = -9\), we need to substitute the point's coordinates into the line equation and compare the results.

### Step-by-Step Solution:

1. **Substitute the point \((1, 3)\) into the line equation:**

   The equation of the line is:
   \[
   3x - 4y = -9
   \]

   Substitute \(x = 1\) and \(y = 3\):

   \[
   3(1) - 4(3) = 3 - 12 = -9
   \]

2. **Compare the result:**

   The result is exactly \(-9\), which matches the right side of the equation.

### Conclusion:
The point \((1, 3)\) lies **on the line** because substituting its coordinates satisfies the line equation.

### Correct Answer:
- The point lies **on the line**.

Would you like more details or have any questions? 

Here are some related questions:
1. How do you find whether a point is above or below a line?
2. What is the general method to find if a point satisfies a linear equation?
3. How can you rewrite the line equation in slope-intercept form?
4. How do parallel lines differ in positioning relative to a point?
5. What happens when multiple points satisfy a line equation?

**Tip:** To determine if a point lies above or below a line, plug the point into the inequality version of the line equation (if needed) to see if it satisfies the condition.

Determine whether the point with coordinates (1, 3) lies on, above or below the line with equation 3x - 4y = -9.

Learn how to determine whether a point lies on, above, or below a given line using the equation 3x - 4y = -9. This problem focuses on coordinate geometry and linear equations, suitable for students in Grades 9-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation