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The graph you provided shows two red lines intersecting on a coordinate plane. I can help you determine the equations of the lines and their intersection point by analyzing the slopes and intercepts.

### Step-by-Step Analysis:
1. **Line 1 (Steeper Slope)**:
   - **Slope**: The line passes through the points \((-5, 5)\) and \((0, -5)\). The slope \(m_1\) is calculated as:
     \[
     m_1 = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-5 - 5}{0 - (-5)} = \frac{-10}{5} = -2
     \]
   - **y-Intercept**: The line crosses the \(y\)-axis at \( (0, -5) \), so the equation is:
     \[
     y_1 = -2x - 5
     \]

2. **Line 2 (Less Steep Slope)**:
   - **Slope**: This line passes through \((5, 5)\) and \((0, -1)\). The slope \(m_2\) is:
     \[
     m_2 = \frac{-1 - 5}{0 - 5} = \frac{-6}{-5} = \frac{6}{5}
     \]
   - **y-Intercept**: It crosses the \(y\)-axis at \((0, -1)\), so the equation of this line is:
     \[
     y_2 = \frac{6}{5}x - 1
     \]

3. **Intersection Point**:
   To find the intersection point, set \(y_1 = y_2\):
   \[
   -2x - 5 = \frac{6}{5}x - 1
   \]
   Let me solve this for \(x\).The \(x\)-coordinate of the intersection point is \(x = -1.25\).

Now, let's substitute this value of \(x\) into one of the line equations (I'll use \(y_1 = -2x - 5\)) to find the \(y\)-coordinate of the intersection point.The intersection point of the two lines is at \((-1.25, -2.5)\).

### Summary:
- **Equation of Line 1**: \( y = -2x - 5 \)
- **Equation of Line 2**: \( y = \frac{6}{5}x - 1 \)
- **Intersection Point**: \( (-1.25, -2.5) \)

Would you like any further details or clarification?

### Related Questions:
1. How do you calculate the slope of a line from two points?
2. What is the importance of the y-intercept in a line equation?
3. How can you solve a system of linear equations graphically?
4. What happens when two lines are parallel in terms of slopes and intersections?
5. How can you verify the solution of a system of equations algebraically?

### Tip:
Always check if two lines have equal slopes before solving them, as equal slopes indicate that the lines are either parallel or the same line.

The graph shows two intersecting red lines on a coordinate plane. What are the equations of the lines and the intersection point?

This page provides a step-by-step solution to determine the equations of two intersecting lines shown in a graph. Learn how to calculate the slope, y-intercept, and find the intersection point using algebraic methods. Suitable for students in Grades 8-10.

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