# Determine the slope of the line that passes through the point (p;q) and (p-4;q+4).

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The slope of a line that passes through the points (x1, y1) and (x2, y2) is given by (y2 - y1)/ (x2 - x1)

Here we have x1 = p , y1 = q , x2 = p - 4 and y2 = q + 4

So the slope is ( q + 4 - q) / ( p - 4 - p)

=> 4 / -4

=> -1

**Therefore the slope is -1.**

To determine the slope of the line that passes through the points (p;q) and (p-4;q+4).

The slope m of the line that passes through (x1,y1) and (x2,y2) if given by:

m = (y2-y1)/(x2-x1).

So the slope of the line passing through (p,q) and (p-4 , q+4) is given by :

slope m = (q+4-q)/(p-4-p)

m = 4/(-4) = -1.

Therefore the slope of the line that passes through the points (p;q) and (p-4;q+4) is -1.

We'll write the formula of the slope of the line that passes through 2 given points:

m=(y2-y1)/(x2-x1)

We'll put x1 = p-4, y1 = q+4 and x2 = p, y2 = q.

We'll substitute them in the formula of the slope:

m = [q - (q + 4)]/[p - (p - 4)]

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

m = (q - q - 4)/(p - p + 4)

We'll eliminate like terms and we'll have:

m = -4/4

m = -1

**The slope of the line that passes through the given points is m = -1.**