Question 731405
The line perpendicular to {{{y= (1/3)x + 4/3}}} will have a slope of -3/1, because perpendicular lines in a plane have slopes which are negative reciprocals of each other.  


Knowing the slope, -3, and the point which must be in this new line, (-2, -6), we can use the point-slope form for a line to write the equation and then simplify:


Point-Slope form for a line
{{{highlight(y-y[0]=m(x-x[0]))}}}
{{{y=m(x-x[0])+y[0]}}}
Substituting coordinate values of the given point to be contained and also the slope,
{{{y=-3(x-(-2))+(-6)}}}
{{{y=-3(x+2)-6}}}
{{{y=-3x-6-6}}}
The line is:______{{{highlight(y=-3x)}}}