First, determine the slope of the radius by the equation,
m = (y₂ - y₁)/ (x₂ - x₁)
Substituting the known values,
m = (1 - -2)/(8 - 4) = 3/4
If the unknown line is perpendicular to this, the slope should be the negative reciprocal which is equal to -4/3. Using the point-slope form to determine the equation,
y - y₁ = m(x - x₁)
Substituting the known values,
y - -2 = (-4/3)(x - 4)
Simplifying,
y + 2 = (-4/3)(x - 4)
3y + 6 = -4x + 16
Answer: 4x + 3y = 10
