First, we need to find the slope:
m=rise/run OR
[tex]m= \frac{y_2-y_1}{x_2-x_1}[/tex]
m=(2+2)/(-6-2)
m=4/-8
m=-1/2
second we need to find the equation for the line using point-slope form:
[tex]y-y_1=m(x-x_1)[/tex]
y-(-2)=-(1/2)(x-2)
[tex]y+2= -\frac{1}{2}x+1[/tex]
[tex]y=- \frac{1}{2}x-1[/tex]
to find "a" we plug in the given y value and solve for x (in this case x=a):
[tex]-4=- \frac{1}{2}x-1[/tex]
[tex]-3=- \frac{1}{2} x[/tex]
[tex]-3(-2)=(- \frac{1}{2} x)( -2)[/tex]
[tex]6=x[/tex]
so, a=6 and the point becomes (6,-4)
