Answer:
a = 6 is the desired value.
Step-by-step explanation:
Let two points be A and B , where A = (2,-2) and B = (-6,2)
Now, slope of the line AB [tex]m= \frac{y_2 - y_1}{x_2 - x_1}[/tex]
or, [tex]m = \frac{2-(-2)}{-6 -2} = \frac{4}{-8} = \frac{-1}{2}[/tex]
So, the slope m = -(1/2)
Now the general form of the equation is given by
y - y0 = m (x-x0) : where (x0, y0) is any point on the line of the equation.
So, here let (x0,y0) = (2, -2) and m = -1/2
The equation becomes : y -(-2) = (-1/2)(x-2)
or, x + 2y = -2 ia the formed equation.
Now here substiture thepoint (a, -4)
we get: a + 2(-4) = -2
or, a = -2 + 8 = 6
or a = 6 is the desired value.
