Question 79518
The slope of a line is the change in Y divided by the change in X, or {{{delta(y)/delta(x)}}}
In the first part, you are given the slope, m, and a single point. So from that information, you know that 
{{{m=delta(y)/delta(x)=(y2-y1)/(x2-x1)}}}
{{{2=(y2-(-1))/(x2-4)}}}
Simplifying...
{{{2=(y2+1)/(x2-4)}}}
Now, you just have to re-write it in the point-slope form, which involves just re-writing the y2 and X2 as y and x respectively and solving for the y+1 term:
{{{2=(y+1)/(x-4)}}}
{{{highlight(y+1=(2)(x-4))}}}
Now that I have shown you how to write a line in point-slope form, you should be able to do the second part.
-------------------------------------------------------------
Write an equation in slope-intercept form of the line having the given slope and passing through the given point:m=-3,(4,-1)
Recall tha slope-intercept forn of a line is:
{{{y=mx+b}}} where m=slope and b=Y-intercept.
So, your first step is to find the Y-intercept:
Remember that:
{{{m=delta(y)/delta(x)=(y2-y1)/(x2-x1)}}}
{{{-3=(y2-(-1))/(x2-4)}}}
The Y-intercept is the point where x2=0. So, equate x2 to zero in the above equation and solve for y2:
{{{-3=(y2+1)/(-4)}}}
{{{12=y2+1}}}
y2=11.
So now that you know the slope and the Y-intercept, it is easy to write the equation:
{{{highlight(y=-3x+11)}}}
With this information, you should be able to do the last part of the problem yourself.
Good Luck,
tutor_paul@yahoo.com