Question 184999
Start with the general linear equation in the "slope-intercept" form:
{{{y = mx+b}}}
Find the slope from the given points (-2,-4) (2,1) using:
{{{m = (y[2]-y[1])/(x[2]-x[1])}}} and the ({{{x[1]}}},{{{y[1]}}}) are the x- and y-coordinates of the first point. Similarly for the second point, so...
{{{m = (1-(-4))/(2-(-2))}}}
{{{m = 5/4}}} Now plug this into the general equation we had at the start.
{{{y = (5/4)x+b}}} Now we need to find the value of b, the y-intercept. This is done by substituting the x- and y-coordinates of either one of the two given points. Let's use the second point (2,1).
{{{y = (5/4)x+b}}} Substitute x = 2 and y = 1 and solve for b.
{{{1 = (5/4)(2)+b}}}
{{{1 = 5/2 + b}}} Subtract {{{5/2}}} from both sides of the equation.
{{{(2/2)-(5/2) = b}}} Simplify.
{{{b = -3/2}}} Now you can write the final equation in slope-intercept form:
{{{highlight(y = (5/4)x-3/2)}}}
A few comments on your work.
It seems that you are having trouble handling the addition/subtraction of positive/negative integers.
Remember...to subtract an integer, you add its additive inverse (opposite), thus:
{{{1-(-4) = 1+(4)}}}={{{5}}} and 
{{{2-(-2) = 2+2}}}={{{4}}}
Furthermore, you came up wth a slope {{{m = 3/0}}} but remember, if a fraction has a zero in the denominator, it considered "undefined" because division by zero is not defined in mathematics.