How do you find the equations of two lines with a point of intersection at (2 , -3) and one of the lines passes through the origin of the system of axes?

1 Answer
Feb 5, 2015

We have one line with two points #(0,0)and(2,-3)#

The equation goes #y=ax+b#

#a_1=(Deltay_1)/(Deltax_1)=(-3-0)/(2-0)=-3/2#

Fill in what you know to find #b_1#

#y_1=a_1x+b_1->-3=-3/2 *2+b_1-> b_1=3#

So the equation of the first line is:

#y_1=-3/2 x+3#

The second line needs more data.
If we know it is perpendicular to the first, then

#a_2=-1/a_1=+2/3#

Fill in what you know to find #b_2#

#y_2=a_2x+b_2->-3=2/3 *2+b_2->b=-4 1/3#

So that equation will be: #2/3 x-4 1/3#