Line A goes through the points (4,5) and (-2,-1) and line B goes through the points (3,3) and (6,1). At what point do they intersect?
I found the equations of the 2 lines, for A I got: $y = 9-x$, and for B I got $y = -\frac{2}{3}x + 5$ and set them equal to each other but it didn't work out.
Best Answer
Denote the lines as $\mathcal{l}_1$ and $\mathcal{l}_2$. The equations of the lines using point slope formula is,
$$\begin{cases}\mathcal{l}_1: \dfrac{y+1}{x+2}=\dfrac{5+1}{4+2}=1\implies x-y+1=0\\ \mathcal{l}_2: \dfrac{y-3}{x-3}=\dfrac{1-3}{6-3}=\dfrac{-2}{3}\implies 2x+3y-15=0\end{cases}$$
Solving the equation of the two lines simultaneously (preferably using cross multiplication) will yield the point of intersection.
I hope you can do the rest by yourself.