The point-slope equation of the line passing through (-2, 6) and (1, 1) is y - 6 = (-5/3)(x + 2).
To find the point-slope equation of the line passing through the points (-2, 6) and (1, 1), we can use the formula:
y - y₁ = m(x - x₁),
where (x₁, y₁) represents the coordinates of one point on the line, and m represents the slope of the line.
First, let's find the slope (m) using the formula:
m = (y₂ - y₁) / (x₂ - x₁),
where (x₁, y₁) = (-2, 6) and (x₂, y₂) = (1, 1):
m = (1 - 6) / (1 - (-2))
= -5 / 3.
Now, we can substitute the values of (x₁, y₁) = (-2, 6), m = -5/3 into the point-slope equation:
y - 6 = (-5/3)(x - (-2)).
Simplifying further:
y - 6 = (-5/3)(x + 2).
Therefore, the point-slope equation of the line passing through (-2, 6) and (1, 1) is y - 6 = (-5/3)(x + 2).