Question 58730
Hi J.B. Gaskins
Find the slope/intercept form of a linear equation that is perpendicular to Y=5x and passes through the point (-5,-5).  Graph both lines to see that they are perpendicular.
:
Perpendicular lines have slopes that are negative reciprocals of each other, they're opposite signs and upside down.
The line that they gave you is in slope intercept form:{{{highlight(y=mx+b)}}}, m=slop, (0,b)=y-intercept.
{{{y=highlight(5)x}}} the slope of this line is m=5
The slope of all lines perpendicular to this line is: m=-1/5
Use the point-slope formula {{{highlight(y-y1=m(x-x1))}}}to find the perpendicular line going through (x1,y1)=(-5,-5).
{{{y-(-5)=(-1/5)(x-(-5))}}}
{{{y+5=(-1/5)(x+5)}}}
{{{y+5=(-1/5)x-(1/5)(5)}}}
{{{y+5=(-1/5)x-1}}}
{{{y+5-5=(-1/5)x-1-5}}}
{{{highlight(y=(-1/5)x-6)}}}
{{{graph(300,200,-15,15,-10,10,5x,(-1/5)x-6)}}}
The red line is y=5x, the green one is y=(-1/5)x-6.  They meet at a 90 degree angle and thus are perpendicular.
Happy Calculating, J.B. Gaskins!!!