Determine the equation of a line passing through the points A(-2,6) and B(2,-4). How do i go about this please explain it in steps.

The equation of a line which passes through 2 given points
is written as it follows:

(xB - xA)/(x-xA) = (yB - yA)/(y -
yA)

xA = -2 and yA = 6

xB = 2
and yB = -4

We'll substitute the coordinates of the given
points into the formula written above:

[(2 -
(-2)]/[(x-(-2)] = (-4 - 6)/(y - 6)

We'll remove the
brackets and we'll get:

(2+2) / (x+2) =
(-10)/(y-6)

4/(x+2)=
-10/(y-6)

Now, we'll cross
multiply:

-10(x+2) =
4(y-6)

We'll remove the
brackets:

-10x - 20 = 4y -
24

We'll move all terms to one
side:

-10x - 4y - 20 + 24 =
0

We'll combine like terms and re-arrange the
terms:

-4y - 10x + 4 = 0

We'll
divide by -2:

2y + 5x - 2 =
0

We've obtained the general form of the equation, that
passes through the given points:

2y + 5x - 2
= 0

We also could put the equation into the
standard form:

2y = -5x +
2

We'll divide by 2 and obtain the standard
form:

y = -5x/2 +
1