The equation of the line passing through points [tex]A(x_1,y_1), B(x_2,y_2)[/tex] is:
[tex]y= \dfrac{y_2-y_1}{x_2-x_1}(x-x_1) +y_1[/tex].
If A(-4,-2) and B(2,0), then
[tex]y= \dfrac{0-(-2)}{2-(-4)}(x-(-4))+(-2) \\ y= \dfrac{2}{6} (x+4)-2 \\ y= \dfrac{1}{3} x- \dfrac{2}{3} [/tex].
If point (a,1) lies on the line
[tex]y= \frac{1}{3} x- \frac{2}{3} [/tex],
then
[tex]1=\dfrac{1}{3} a- \dfrac{2}{3} \\ \dfrac{5}{3} =\dfrac{1}{3} a \\ a=5[/tex].
Answer: [tex]y= \frac{1}{3} x- \frac{2}{3} [/tex], a=5.
