To find the equation of the line in slope-intercept form, we first need to determine the slope and the y-intercept from the graph.
The slope is the change in y divided by the change in x between two points on the line. We can choose two points on the line and calculate the slope using the formula:
slope = (y2 - y1) / (x2 - x1)
Let's choose the points (0, 12) and (4, 4) on the line:
slope = (4 - 12) / (4 - 0)
slope = -8 / 4
slope = -2
So, the slope of the line is -2.
Next, we need to find the y-intercept, which is the value of y when x = 0. From the graph, we can see that the y-intercept is 12.
Now we can write the equation of the line in slope-intercept form:
y = mx + b
where m is the slope and b is the y-intercept. So, substituting m = -2 and b = 12, we get:
y = -2x + 12
Therefore, the equation of the line in slope-intercept form is y = -2x + 12.