Question 70222
To find the slope from A(-1, -9)to B(6, 12) use
{{{m=(12-(-9))/(6-(-1))}}}
{{{m=21/7}}}
{{{m=3}}}
Now use the general slope-intercept equation of a line y=mx+b and solve for b.
{{{12=3(6)+b}}}Plug in point  B(6,12) either point will work
{{{12-18=b}}}
{{{b=-6}}}
So the equation is 
{{{y=3x-6}}}
To find the equation from C to D, we need to invert and negate the slope of our previous answer. This makes the new slope perpendicular to the old slope.
{{{m=-1/3}}}
Now plug in the point C to solve for b
{{{-5=(-1/3)(7)+b}}}
{{{-5+7/3=b}}}
{{{b=-8/3}}}
So the equation of the line that passes through CD is 
{{{y=(-1/3)x-8/3}}}
To verify this answer, you can graph these lines and plot the points. A good program for this on the PC is Winplot (http://math.exeter.edu/rparris/winplot.html ) which allows quick and efficient graphing, and allows you to plot points.