Answer:
k = - 1
Step-by-step explanation:
calculate the gradient (slope) m of AB using the slope formula and equate to 4
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (- 3, 4 ) and (x₂, y₂ ) = (k, 12 )
m = [tex]\frac{12-4}{k-(-3)}[/tex] = [tex]\frac{8}{k+3}[/tex] , then
[tex]\frac{8}{k+3}[/tex] = 4 ( multiply both sides by (k + 3 ) )
4(k + 3) = 8 ( divide both sides by 4 )
k + 3 = 2 ( subtract 3 from both sides )
k = - 1
