slope/Point problem.?

Apply slope formula

Given 

m = -3

points P1(1 - a, 3) and P2(3,2 + a)

.........y₂ - y₁

m= ------------

........x₂ - x₁

..........2 + a - 3

- 3 =---------------

..........3 - (1 - a)

.........a - 1

- 3 =--------------

..........2 + a

- 3(2 + a) = a - 1

 - 6 - 3a = a - 1

 - 6 + 1 = a + 3a

 - 5 = 4a

a = - 5/4 Answer//

The slope is the (difference in y-coordinates) divided by (difference in x-coordinates).

[(2+a)-3] / [3-(1-a)] = -3

(a-1)/ (a+2) = -3

a-1 = -3a-6

4a = -5

a = -5/4

You can determine the slope given two points by taking the change in y over the change in x.  If the points are:

(1 - a, 3) and (3, 2 + a)

Then the change in y is:

(2 + a) - 3

and the change in x is:

3 - (1 - a)

divide one from the other, set it equal to -3, then solve for a:

[(2 + a) - 3] / [3 - (1 - a)] = -3

Simplify both halves of the fraction:

(2 + a - 3) / (3 - 1 + a) = -3

(a - 1) / (a + 2) = -3

Multiply both sides by (a + 2)

a - 1 = -3(a + 2)

simplify:

a - 1 = -3a - 6

Add 3a and 1 to both sides:

4a = -5

divide both sides by 4:

a = -5/4