To find the point-slope equation of a line passing through two points, we can use the formula:
y - y₁ = m(x - x₁)
Where (x₁, y₁) and (x₂, y₂) are the coordinates of the two points, and m is the slope of the line.
Given the points (-2,6) and (1,1), we need to find the slope first. The slope (m) is calculated using the formula:
m = (y₂ - y₁) / (x₂ - x₁)
Substituting the coordinates of the points:
m = (1 - 6) / (1 - (-2))
m = -5 / 3
Now we can substitute one of the given points and the slope into the point-slope equation:
y - 1 = (-5/3)(x - 1)
This is the complete point-slope equation of the line passing through the points (-2,6) and (1,1).