Question 66134
The first thing you can do is to find the slope of the line that passes through the given pair of points.
The slope, m, can be found by:
{{{m = (y2-y1)/(x2-x1)}}} where (x1, y1) and (x2, y2) are the coordinates of the two given points through which the lines passes. So, let's find the slope.
{{{m = (-2-3)/(4-(-1))}}} Simplify this.
{{{m = -5/5}}}
{{{m = -1}}} This is the slope of the line, so now you can start writing the equation of the line in slope-intercept form {{{y = mx+b}}}:
{{{y = (-1)x + b}}} but now we need to find the value of b, the y-intercept.  We can do this by substituting the x- and y-coordinates of either one of the two given points and solving for b. Let's choose the second point (4, -2).
{{{-2 = (-1)(4) + b}}} Simplify this.
{{{-2 = -4+b}}} Add 4 to both sides.
{{{2 = b}}} This is the value of b, the y-intercept. Now we can finish writing the equation:
{{{y = (-1)x + 2}}} or
{{{y = -x + 2}}}