Question

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 1

First, we need to find the slope:
m=rise/run   OR
$m= \frac{y_2-y_1}{x_2-x_1}$
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:
$y-y_1=m(x-x_1)$

y-(-2)=-(1/2)(x-2)
$y+2= -\frac{1}{2}x+1$
$y=- \frac{1}{2}x-1$

to find "a" we plug in the given y value and solve for x (in this case x=a):

$-4=- \frac{1}{2}x-1$
$-3=- \frac{1}{2} x$
$-3(-2)=(- \frac{1}{2} x)( -2)$
$6=x$

so, a=6 and the point becomes (6,-4)