# A line contains the points (a-4, b+4) and (a, b). What is the slope of the line.

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Given the points: ( a-4) , b+4) and ( a,b)

We need to determine the slope of the line passes through the points:

We will use the slope formula:

m = ( y2-y1) / (x2- x1) such that:

(x1,y1) and (x2,y2) are points of the line:

==> m = ( b+4 - b) / ( a-4 -a)

Then we will reduce similar:

==> m = 4 / -4 = -1

==? m = -1

**Then the slope of the line passes through the points is m = -1**

The equation of the line passing through (a-4 , b+4) and (a , b) is

y - (b + 4) = [( b - (b + 4)) / (a - (a -4))] ( x - (a - 4))

=> y - b - 4 = [ - 4 / 4] ( x - (a - 4))

=> y = -x + a - 4 + b + 4

=> y = -x + a + b

This equation is of the form y = mx +c, where the slope of the line is m and c is the y- intercept.

**Therefore the slope of the given line is -1.**

The slope m of the line that joins any two points (x1,y1) and (x2,y2) is given by:

m = (y2-y1)/(x2-x1)....(1)

The given two points are (a-4 , b+4) and (a,b).

Here x1 = a-4 , y1 = b+4 and x2 = a and y2 = b.

Therefore ,we substitute the coordintes of the given points in the formula at (1) to obtain the slope.

m = {b-(b+4)}/{a- (a-4)}.

m = (-4)/(4).

m = -1.

Therefore the slope of the line joining the points (a-4, b+4) and (a , b) is -1.

The slope of the line that passes through 2 given points has the formula:

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

We'll put x1 = a-4, y1 = b+4 and x2 = a, y2 = b.

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

m = [b-(b+4)]/[a - (a-4)]

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

m = (b-b-4)/(a-a+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.**