Question 23238
Anytime you have a line, you need three formulas:

Formula 1:  slope: m = {{{(y2 - y1)/(x2 - x1)}}}

Formula 2:  point slope form:  y - y1 = m(x-x1)

Formula 3:  slope intercept form:  y = mx + b

(x1,y1) and (x2,y2) are two points on your line, m is the slope, and b is the y intercept.

So for your first problem, the two points we're looking at are (8,2) and (4,-7).  Using the first formula, m = {{{(-7-4)/(2-8)}}} = {{{(-13)/(-6)}}} = {{{13/6}}}.  Now we use the second formula to get the line you want.  The equation for the line will be y - 2 = {{{13/6}}}(x-8).  If you want it in y = mx+b form, add two to both sides and distribute the {{{13/6}}} to get y = {{{13/6}}}x - {{{46/3}}}.

For the second one, the first formula can be skipped since we already know the slope.  So the equation becomes y - 4 = -4(x-4).  Again if you want the y = mx+b  form, solve for y to get y = -4x + 20.

For the third one, using the third formula gives us that the line is y = 3x + 5.

The fourth one requires a little work.  Using the third formula, we have that y = 3x + b, where b is the y intercept.  But we do not know the y intercept in this case so we don't know b just yet.  However we do know that the x intercept is 5.  This means that if we plug zero in for y, then we should get an x value of 5.  So using this, we have 0 = 3*(5) + b, so 0 = 15 + b, and thus b = -15.  Therefore our line is y = 3x - 15.