2
$\begingroup$

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.

$\endgroup$
  • 1
    $\begingroup$ 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
  • 1
    $\begingroup$ so the answer is (12/5,17/5)???? $\endgroup$ – Mandy Stevens Apr 4 '15 at 5:53
1
$\begingroup$

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.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.