Answer:
D
Step-by-step explanation:
the equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b) a point on the line
to calculate m use the gradient formula
m = ( y₂ - y₁ ) / ( x₂ - x₁ )
with (x₁, y₁ ) = (6, - 3) and (x₂, y₂ ) = (- 4, - 9)
m = [tex]\frac{-9+3}{-4-6}[/tex] = [tex]\frac{-6}{-10}[/tex] = [tex]\frac{3}{5}[/tex]
using (- 4, - 9) or (6, - 3) for (a, b)
using (- 4, - 9), gives
y + 9 = [tex]\frac{3}{5}[/tex](x + 4) ← not one of the options
using (6, - 3), gives
y + 3 = [tex]\frac{3}{5}[/tex](x - 6) ← option D
