The image you provided shows a problem related to the travel distance over time, presented with a graph and some questions about slope and equations. Here's a breakdown of the key points from the image:

1. Graph Interpretation:

   • The graph shows the relationship between time (x-axis, in hours) and distance (y-axis, in miles). The line is descending, indicating a reduction in distance over time, suggesting that this is likely modeling something like a trip where the distance is reduced over time.
   • The graph passes through two key points: $(0, 360)$ and $(6, 0)$.

2. Slope Calculation:

   • Slope $m$ is calculated as the change in $y$ (distance) over the change in $x$ (time), using the formula: $m = \frac{y_2 - y_1}{x_2 - x_1}$ Using the points $(0, 360)$ and $(6, 0)$: $m = \frac{0 - 360}{6 - 0} = \frac{-360}{6} = -60$ So, the correct slope is $-60$, but the student incorrectly wrote $8$, and it was corrected to the right slope $-60$.

3. Equation of the Line:

   • The general form of the line is $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.
   • The slope $m = -60$, and the y-intercept $b = 360$, since the line crosses the y-axis at $y = 360$.
   • Therefore, the correct equation of the line should be: $y = -60x + 360$
   • The student wrote $y = 6x + 360$, which was corrected to $-60$.

4. Interpretation of Slope:

   • The slope of $-60$ represents the rate at which distance decreases per hour. In this context, it means that the object or traveler is reducing the distance by 60 miles for every hour of travel.
   • The student originally stated that the slope represents "time", but the correct interpretation is that the slope represents "distance traveled per hour" (rate of change of distance with respect to time).

Would you like more details or further explanations on any part of this?

Here are 5 related questions you might find helpful:

1. How is the slope of a line determined when given two points?
2. What is the meaning of a negative slope in a real-world context?
3. How can you find the y-intercept of a line from a graph?
4. How do we use the slope-intercept form to model linear relationships in real life?
5. What are some real-life situations where linear equations like this one are useful?

Tip: Always double-check your slope calculations by carefully identifying the rise (change in $y$) and run (change in $x$) to avoid sign errors!