This graph shows a straight line passing through the coordinate plane. To interpret and find the equation of the line, we can extract key points and use them to determine the slope and the y-intercept.

1. Identify two points on the line:

   • From the graph, we can see two points where the line crosses grid points clearly:
     • The first point is approximately at $(0, 6)$ (the y-intercept).
     • The second point is approximately at $(2, 4)$.

2. Calculate the slope (m): The slope is calculated as the change in $y$ divided by the change in $x$: $m = \frac{y_2 - y_1}{x_2 - x_1}$ Using the points $(0, 6)$ and $(2, 4)$: $m = \frac{4 - 6}{2 - 0} = \frac{-2}{2} = -1$

3. Find the equation of the line: Using the slope-intercept form $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept:

   • The slope $m = -1$ and the y-intercept $b = 6$. Thus, the equation of the line is: $y = -x + 6$

Would you like further details or explanations on this? Here are some related questions to deepen your understanding:

1. How can you calculate the slope of a line if given two arbitrary points?
2. What is the importance of the y-intercept in the equation of a line?
3. How can you convert a linear equation from standard form to slope-intercept form?
4. What is the relationship between the slope of a line and the steepness of its graph?
5. How can you graph a line given its equation?

Tip: When calculating slope, always pay attention to the signs of the changes in $y$ and $x$ to ensure accuracy in direction (positive or negative slope).