Question 60981
The distance between two points if found by computing the hypotenuse of a right triangle using the Pythagorean Theorem {{{c^2 = a^2 + b^2}}}.
In the case of P and Q, the length of one side of the triangle is found by calculating the distance between X values and the length of another side is found by calculating the distance between the Y values.
So, the y values are 2 and -3 and their difference is {{{2-(-3) = 5}}}.
The y values are 9 and 3. Their difference {{{9-3 = 6}}}.
Use the Pythagorean Theorem to find the shortest distance between these points, the hypotenuse of the triangle with sides 5 and 6. 
{{{c^2 = 5^2 + 6^2}}}. So, {{{c^2 = 5^2 + 6^2 = 61}}} so {{{c = sqrt(61)}}} which is approximately {{{7.81}}} and that's the distance between the two points.

The formula for a line is {{{y=mx+b}}} where x is the slope and b is the y-axis intercept. The slope is the ratio of the change in x to the change in y.
We know from our work above that the x increases by 6 for every increase in 5 that the y goes up. 
So, the slope is: {{{ m = 6/5 = 1.2}}}.
So, the equation of the line is: {{{ y=(6/5)x+b}}}.
We need to find x.
We can use the x and y values of either point to do that.
Using Q, (-3,3) we find that {{{ 3=(6/5)(-3)+b}}}.
Or, {{{3 = -(18/5) + b}}}
Or, {{{3+(18/5) = b}}}.
So, {{{b=6.6}}}.
Thus, the equation of the line is {{{y=1.2x+6.6}}}.

We verify this with both points:

If x = -3 and y = 3 then {{{y=1.2(-3)+6.6}}} so {{{y=-3.6+6.6=3}}}.
If x = 2 and y = 9 then {{{y=1.2(2)+6.6}}} so {{{y=2.4+6.6=9}}}.