Question 87837
You can start with the formula for finding the slope, m, of a line that passes through two points, (x1, y1) and (x2, y2):
{{{m = (y[2]-y[1])/(x[2]-x[1])}}}
You are given the slope, m = 3.
And the two points are: 
(x1, y1) = (k+2, k) and
(x2, y2) = (3, 2)
Now if you substitute the given values into the formula, you can solve for k.
{{{3 = (2-k)/(3-(k+2))}}} Simplify this.
{{{3 = (2-k)/(3-k-2)}}} Notice the change of sign on the 2 in the denominator.
{{{3 = (2-k)/(1-k)}}} Now multiply both sides by (1-k).
{{{3(1-k) = 2-k}}} Apply the distributive property on the left side.
{{{3-3k = 2-k}}}  Add 3k to both sides.
{{{3 = 2+2k}}} Subtract 2 from both sides.
{{{1 = 2k}}} Finally, divide both sides by 2.
{{{1/2 = k}}}
Answer is:
{{{k = 1/2}}}

Let's check the answer by substituting{{{k = 1/2}}} into the slope formula.
{{{m = (2-(1/2))/(3-((1/2)+2))}}} Simplifying this, we get:
{{{m = (3/2)/(3-(5/2))}}}
{{{m = (3/2)/(1/2)}}}
{{{m = 3}}} ...and this is the expected slope!