From the image, the task is to write an equation in slope-intercept form of the line shown on the graph. The slope-intercept form of a line is expressed as:

$y = mx + b$

where $m$ is the slope and $b$ is the y-intercept.

Let's determine the slope ($m$) first. The slope can be calculated by selecting two points on the line and using the formula:

$m = \frac{\text{change in y}}{\text{change in x}} = \frac{y_2 - y_1}{x_2 - x_1}$

From the graph, we can select the points (1, 3) and (3, 1). Plugging these into the formula:

$m = \frac{1 - 3}{3 - 1} = \frac{-2}{2} = -1$

Next, the y-intercept ($b$) is the point where the line crosses the y-axis. Observing the graph, the line crosses the y-axis at $y = 5$. Therefore, $b = 5$.

Combining these, the equation of the line in slope-intercept form is:

$y = -1x + 5$

Or simply:

$y = -x + 5$

Would you like more details on how to find the slope or y-intercept from a graph? Do you have any questions?

1. Would you like to see another example of writing an equation from a graph?
2. Do you need clarification on how the y-intercept is identified on a graph?
3. Are you interested in learning about different forms of linear equations?
4. Would you like to know how to check if a point lies on this line?
5. Are there other types of equations or graphs you're curious about?

Tip: When choosing points from a graph to calculate the slope, it's often useful to pick points where the line crosses grid lines to ensure accuracy.