From the graph provided:

The plot appears to model a linear relationship between the study time (x-axis) and the score (y-axis). To determine the linear equation that best fits the model, we need to estimate:

1. The slope (m): The rate at which the score increases with study time.
2. The y-intercept (b): The score when study time is 0.

Step 1: Estimate the slope

From the graph:

• At $x = 0.5$, $y \approx 40$.
• At $x = 4.5$, $y \approx 90$.

The slope $m$ is calculated as: $m = \frac{\Delta y}{\Delta x} = \frac{90 - 40}{4.5 - 0.5} = \frac{50}{4} = 12.5$

Step 2: Estimate the y-intercept

The y-intercept ($b$) is where the line crosses the y-axis ($x = 0$). From the graph, it appears to intersect near $y = 40$.

Step 3: Write the equation

The equation of the line can be written in slope-intercept form: $y = mx + b$ Substituting the values of $m = 12.5$ and $b = 40$: $y = 12.5x + 40$

Final Answer:

The linear equation that best describes the given model is: $y = 12.5x + 40$

Let me know if you'd like more details or a breakdown of the calculations!

Follow-Up Questions:

1. How is the slope determined in a linear equation?
2. Why does the y-intercept matter in the context of this model?
3. Could this model be used to predict scores for study times outside the range in the graph? Why or why not?
4. What does the slope indicate about the relationship between study time and score?
5. How would errors in the data points affect the equation of the line?

Tip: Always verify your slope calculation using multiple points to confirm consistency!