To find the equation of the line in point-slope form that passes through the points (3, 6) and (2, 1), we first need to calculate the slope of the line. The slope (m) can be found using the formula:
m = (y2 – y1) / (x2 – x1)
Here, we will designate (x1, y1) as (3, 6) and (x2, y2) as (2, 1):
m = (1 – 6) / (2 – 3) = -5 / -1 = 5
Now that we have the slope, we can use the point-slope formula for the equation of a line, which is:
y – y1 = m(x – x1)
We can choose either of the two points to use in the equation. Let’s pick the point (3, 6):
y – 6 = 5(x – 3)
This can be considered the point-slope form of the line through the points (3, 6) and (2, 1). To write it more cleanly, the final equation is:
y – 6 = 5(x – 3)