Question 104045
The general form is y = mx+b where m is the slope and b is the y-intercept.
Let's first find the slope using the slope formula:
{{{m = (y[2]-y[1])/(x[2]-x[1])}}} The {{{x[1]}}},{{{y[1]}}},{{{x[2]}}}, and {{{y[2]}}} are the coordinates of the given points (4, 3) and (-4, -4).
Making the appropriate substitutions, we get:
{{{m = (-4-3)/(-4-4)}}}
{{{m = (-7)/-8}}}
{{{m = 7/8}}}
So we can write the first step of the equation using the slope:
{{{y = (7/8)x+b}}} Now we need to find the value of b, the y-intercept.
This is done by substituting, in the preceding equation, the x- and y-coordinates of either one of the two given points. Let's use point (4, 3) in which x = 4 and y = 3.  Making the appropriate substitutions, we get:
{{{3 = (7/8)(4)+b}}} Simplify and solve for b.
{{{3 = 7/2 + b}}} Subtract 7/2 from both sides. 
{{{6/2 - 7/2 = b}}}
{{{b = -1/2}}}
Now we can write the final equation:
{{{y = (7/8)x-1/2}}}
Here's the graph:
{{{graph(600,400,-5,5,-5,5,(7/8)x-2)}}}