Question 559671
You could write the rule in the form of a "slope-intercept" linear equation: {{{y = mx+b}}} by finding the slope;
{{{m = (y[2]-y[1])/(x[2]-x[1])}}} Use the x- and y-coordinates of the two given points (-6, 4) and (3, -8) as the inputs.
{{{m = (-8-4)/(3-(-6))}}}
{{{m = (-12)/9}}}
{{{m = -4/3}}} so you have:
{{{y = (-4/3)x+b}}} To find b, substitute the x- and y-coordintes from either one of the given points. Say (3, -8).
{{{-8 = (-4/3)*3+b}}}
{{{-8 = -4+b}}} Add 4 to both sides.
{{{-4 = b}}} now you write the finished equation (rule):
{{{y = (-4/3)x-4}}}