Answer:
A
Step-by-step explanation:
Calculate the slope of the given points with the point (- 2, 5 )
If the slope is - [tex]\frac{3}{4}[/tex] then the point is on the line
Calculate slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 2, 5) and (x₂, y₂ ) = (6, - 1)
m = [tex]\frac{-1-5}{6+2}[/tex] = [tex]\frac{-6}{8}[/tex] = - [tex]\frac{3}{4}[/tex] ← point (6, - 1) is on the line
Repeat with (x₁, y₁ ) = (- 2, 5 ) and (x₂, y₂ ) = (2, 8)
m = [tex]\frac{8-5}{2+2}[/tex] = [tex]\frac{3}{4}[/tex] ← point (2, 8) is not on the line
Repeat with (x₁, y₁ ) = (- 2, 5) and (x₂, y₂ ) = (- 5, 1)
m = [tex]\frac{1-5}{-5+2}[/tex] = [tex]\frac{-4}{-3}[/tex] = [tex]\frac{4}{3}[/tex] ← point (- 5, 1) is not on the line
Repeat with (x₁, y₁ ) = (- 2, 5) and (x₂, y₂ ) = (1, 1)
m = [tex]\frac{1-5}{1+2}[/tex] = - [tex]\frac{4}{3}[/tex] ← point (1, 1) is not on the line
Thus the point on the line is (6, - 1 ) → A
