To find the equation of the line in slope-intercept form, we need to determine the slope (m) and the y-intercept (b) of the line.

1. Identify Two Points: From the graph, the line passes through approximately:

   • Point A at (0, 9) (this is the y-intercept),
   • Another point, such as (2, 7).

2. Calculate the Slope (m): The formula for the slope between two points $(x_1, y_1)$ and $(x_2, y_2)$ is: $m = \frac{y_2 - y_1}{x_2 - x_1}$ Using the points (0, 9) and (2, 7): $m = \frac{7 - 9}{2 - 0} = \frac{-2}{2} = -1$

3. Determine the y-Intercept (b): Since the line passes through (0, 9), the y-intercept $b$ is 9.

4. Write the Equation: Now, we can write the equation in slope-intercept form $y = mx + b$: $y = -x + 9$

So, the equation of the line is: $y = -x + 9$

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

Related Questions

1. How do we determine the slope of a line from two points?
2. What does the y-intercept represent in a graph?
3. Can a line have a positive slope if it’s sloping downwards?
4. How would the equation change if the line passed through a different y-intercept?
5. How can you verify the slope and y-intercept using the graph?

Tip

When writing equations of lines, remember that the y-intercept is where the line crosses the y-axis, and the slope determines the direction and steepness of the line.