# Find the intersection of two lines passing through given points

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.

• The line $y=9-x$ does not pass through $(-2,-1)$. Re-check your computation of line A. – user147263 Apr 4 '15 at 5:46
• I did and used the point slope formula. dont get it – Mandy Stevens Apr 4 '15 at 5:47
• I think you got the sign wrong on the slope, which then got you the wrong intercept as well. Note then when $x$ increases from $-2$ to $4$, $y$ also increases from $-1$ to $5$, so the slope has to be positive. – Callus Apr 4 '15 at 5:51
• slope of A $=\frac{-1-5}{-2-4}=\frac{-6}{-6}=1$ – Vikram Apr 4 '15 at 5:53
• so the answer is (12/5,17/5)???? – Mandy Stevens Apr 4 '15 at 5:53

Denote the lines as $\mathcal{l}_1$ and $\mathcal{l}_2$. The equations of the lines using point slope formula is,
$$\begin{cases}\mathcal{l}_1: \dfrac{y+1}{x+2}=\dfrac{5+1}{4+2}=1\implies x-y+1=0\\ \mathcal{l}_2: \dfrac{y-3}{x-3}=\dfrac{1-3}{6-3}=\dfrac{-2}{3}\implies 2x+3y-15=0\end{cases}$$