Question

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?

Answer 1

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`