A line passes through the points (2, –2) and (–6, 2). The point (a, –4) is also on the line. What is the value of a?

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  = -1/2The 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) = -2or, a = -2 + 8 = 6or a = 6 is the desired value.