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?

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Answer 1 · 2015-02-05T17:00:41

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: $2/3 x-4 1/3$