n = 4
calculate the slope m using the gradient formula
m = (y₂ - y₁ ) / (x₂ - x₁ )
with (x₁, y₁ ) = (8, - 4 ) and (x₂, y₂ ) = (10, n )
m = [tex]\frac{n+4}{10-8}[/tex] = [tex]\frac{n+4}{2}[/tex]
now m = 4, hence
[tex]\frac{n+4}{2}[/tex] = 4 ( multiply both sides by 2 )
n + 4 = 8 ( subtract 4 from both sides )
n = 4
If a slope of the line is 4, then the equation of the line is
y=4x+b.
This line passes through the point (8,-4), this means that coordinates of this point satisfy the equation:
-4=4·8+b,
b=-4-32,
b=-36.
Thus, the equation of the line is y=4x-36.
Now, substitute the coordinates of the point (10,n) into the equation:
n=4·10-36,
n=40-36,
n=4.
Answer: n=4.
