Show that the coordinates of S are 𝑆(0,−2)

To show that the coordinates of point \( S \) are \( S(0, -2) \), you would typically need some information about the problem context, such as equations of lines, a geometric description, or specific points through which \( S \) is defined. However, since no specific context is provided, I'll outline a general process to determine how one might demonstrate that a point \( S \) has coordinates \( (0, -2) \) using a couple of scenarios:

### Scenario 1: \( S \) is the Y-intercept of a Line
If \( S \) is the y-intercept of a line, then \( S \) has an \( x \)-coordinate of 0. To find the \( y \)-coordinate:

1. **Equation of the line**: Suppose the line is given by \( y = mx + c \).
2. **Substitute \( x = 0 \)**: When \( x = 0 \), \( y = c \), so \( S(0, c) \).
3. **Given that \( c = -2 \)**: We conclude that \( S = (0, -2) \).

### Scenario 2: \( S \) is a Point on the Y-axis
If \( S \) is defined as being on the y-axis and given its \( y \)-coordinate:

1. **Given information**: Suppose \( S \) is given as a point on the y-axis with \( y = -2 \).
2. **Coordinates of \( S \)**: Since \( S \) is on the y-axis, \( x = 0 \).
3. **Conclusion**: The coordinates of \( S \) are \( S(0, -2) \).

### Scenario 3: \( S \) as a Solution to a System of Equations
If \( S \) is the solution to a system of linear equations, substitute \( x = 0 \) and find \( y \):

1. **Given system of equations**:
   - \( ax + by = c \)
   - \( dx + ey = f \)
2. **Substitute \( x = 0 \)** in both equations to solve for \( y \).
3. **Solve**: If \( y = -2 \), then \( S(0, -2) \) is the solution.

These are general methods for proving the coordinates of \( S \). The exact approach depends on the context or given problem.

Would you like more details or have any questions? Here are some related questions:

1. How do you find the y-intercept of a line given its equation?
2. What are the steps to solve a system of linear equations?
3. How can you determine the intersection point of two lines?
4. What are the conditions for a point to lie on the y-axis?
5. How can you verify if a point lies on a given line?

**Tip:** Always check if the point satisfies the given conditions or equations to confirm its coordinates.

Learn how to demonstrate that the coordinates of point S are (0, -2) using scenarios such as finding the y-intercept of a line or identifying a point on the y-axis. Explore different mathematical methods to prove the coordinates of a given point. Suitable for high school students and learners interested in coordinate geometry.

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