https://file.aiquickdraw.com/mathbot/file/1727394641878r4bya5f3.jpg

Let's solve for the equations of the lines based on the provided graph. The two lines intersect at a specific point and have clear slopes.

We can write the equation of a line in the slope-intercept form: 

\[
y = mx + b
\]

where \( m \) is the slope and \( b \) is the y-intercept.

### Brown Line
1. **Y-intercept**: The brown line crosses the y-axis at \( y = -7 \).
   
2. **Slope**: The line decreases as we move to the right, so the slope is negative. By counting the rise over run between two points (e.g., from (0, -7) to (5, -1)), we find the slope \( m \):
   \[
   m = \frac{(y_2 - y_1)}{(x_2 - x_1)} = \frac{-1 - (-7)}{5 - 0} = \frac{6}{5}
   \]
   Thus, the slope of the brown line is \( m = \frac{6}{5} \).

Therefore, the equation of the brown line is:
\[
y = \frac{6}{5}x - 7
\]

### Blue Line
1. **Slope**: The slope is given as \( -\frac{4}{5} \).

2. **Y-intercept**: To find the y-intercept, we can look at where the blue line crosses the y-axis. It appears to cross at \( y = 4 \).

Therefore, the equation of the blue line is:
\[
y = -\frac{4}{5}x + 4
\]

### Final Equations
- Brown line: \( y = \frac{6}{5}x - 7 \)
- Blue line: \( y = -\frac{4}{5}x + 4 \)

Do you have any questions or want more details on these calculations?

Here are 5 related questions:
1. How can you determine the slope of a line using two points?
2. What is the significance of the y-intercept in a linear equation?
3. How do positive and negative slopes affect the direction of a line on a graph?
4. Can you derive the equation of a line from its slope and a point on the line?
5. How can parallel or perpendicular lines be identified from their slopes?

**Tip**: When calculating slope, always remember that it represents "rise over run" or how much the line goes up/down per unit of movement horizontally.

Find the equations of the lines from the graph provided, with exact numbers.

Learn how to find the equations of two lines from a graph, using the slope-intercept form (y = mx + b). This example covers finding the slope and y-intercept of both lines and writing their equations step-by-step. Suitable for students in Grades 7-10.

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