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.

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    $\begingroup$ The line $y=9-x$ does not pass through $(-2,-1)$. Re-check your computation of line A. $\endgroup$ – user147263 Apr 4 '15 at 5:46
  • $\begingroup$ I did and used the point slope formula. dont get it $\endgroup$ – Mandy Stevens Apr 4 '15 at 5:47
  • $\begingroup$ 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. $\endgroup$ – Callus Apr 4 '15 at 5:51
  • $\begingroup$ slope of A $=\frac{-1-5}{-2-4}=\frac{-6}{-6}=1$ $\endgroup$ – Vikram Apr 4 '15 at 5:53
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    $\begingroup$ so the answer is (12/5,17/5)???? $\endgroup$ – 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,

$$\begin{cases}\mathcal{l}_1: \dfrac{y+1}{x+2}=\dfrac{5+1}{4+2}=1\implies x-y+1=0\\ \mathcal{l}_2: \dfrac{y-3}{x-3}=\dfrac{1-3}{6-3}=\dfrac{-2}{3}\implies 2x+3y-15=0\end{cases}$$

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.


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