a = [tex]\frac{1}{4}[/tex]
using the ' gradient formula ' m = (y₂ - y₁)/(x₂ - x₁) → (m is the slope)
here (x₁, y₁) = (a , - 2)) and (x₂ , y₂) = (- 2, 7)
thus [tex]\frac{(7 + 2)}{(-2 - a)}[/tex] = -4 ⇒[tex]\frac{9}{(- 2 - a)}[/tex] = -4
cross-multiply
-4(- 2 - a) = 9
8 + 4a = 9
subtract 8 from both sides
4a = 9 - 8 = [tex]\frac{1}{4}[/tex]1
divide both sides by 4
a = [tex]\frac{1}{4}[/tex]
