To find the equation of the line in the form $y = mx + b$, we need to determine two things from the graph:

1. The slope $m$, which represents the "rise over run."
2. The y-intercept $b$, which is the point where the line crosses the y-axis.

Step 1: Identify the y-intercept ($b$)

From the graph, it appears that the line crosses the y-axis at $y = 10$. Therefore: $b = 10$

Step 2: Calculate the slope ($m$)

To find the slope, we can pick two points on the line. Based on the graph, two clear points are:

• $(0, 10)$, where the line crosses the y-axis.
• $(10, 0)$, where the line crosses the x-axis.

The formula for the slope $m$ is: $m = \frac{{y_2 - y_1}}{{x_2 - x_1}}$

Substitute $(x_1, y_1) = (0, 10)$ and $(x_2, y_2) = (10, 0)$: $m = \frac{{0 - 10}}{{10 - 0}} = \frac{{-10}}{{10}} = -1$

Conclusion

The equation of the line is: $y = -x + 10$ with $m = -1$ and $b = 10$.

Would you like further explanation on any part of this process?

Additional Related Questions:

1. How would the equation change if the line had a different y-intercept?
2. What happens to the slope if the line is steeper?
3. How do you find the equation if the line passes through two arbitrary points?
4. What if the line is horizontal or vertical—what would the equation look like?
5. How can you verify that the points you chose are accurate for calculating the slope?

Tip: When identifying the slope from a graph, always double-check the rise and run between two points for accuracy.