How do you calculate angle between $\frac{x}{5}+\frac{y}{3}=1$ and $x=-1$?

Question

What I did: I rewrote $\frac{x}{5}+\frac{y}{3}=1$ as $y=3-\frac{3x}{5}$, therefore $m_{1}$ is $-\frac{3}{5}$, but what is $m_{2}$ of $x=-1$? It doesn't exist, right?

How do I then calculate angle if there's no $m_{2}$?

Formula which I would use to calculate the angle (if γ is an angle): $tanγ=|\frac{m_{2}-m_{1}}{1+m_{1}\cdot m_{2}}|$

The formula will work, if we take $m_1=-3/5$ and find $\lim_{m_2\to\infty}\left|\frac{m_2-m_1}{1+m_2m_1}\right|$. — André Nicolas, Feb 03 '14 at 16:48

score 1 · Accepted Answer · answered Feb 03 '14 at 16:29

1

The equation $x = -1$ is just a vertical line. So you have a line with slope $-3/5$ and you want to find the angle that it makes with a vertical line. That means you can consider a right-angled triangle with sides $1$ and $3/5$. Or with scaling you have a triangle with sides $5$ and $3$.

answered Feb 03 '14 at 16:29

Thomas

43,555

I solved it! Thank you very much! :) – L_McClain Feb 03 '14 at 16:44

How do you calculate angle between $\frac{x}{5}+\frac{y}{3}=1$ and $x=-1$?

1 Answers1