Question

Find an equation for the line below.A(5,1) B(-4,5)

Answer 1

The equation of a line has always the form

$y=m\cdot x+b$

where "m" is called its slope, and "b" is called its y-intercept. It's a well-known fact that m can be calculated using two points of the line. Let's use A and B:

$m=\frac{-5-1}{-4-(5)}=\frac{-6}{-9}=\frac{6}{9}=\frac{2}{3}$

Then, our equation becomes

$y=\frac{2}{3}x+b$

Replacing A there, we get

$\begin{gathered} 1=\frac{2}{3}(5)+b\Rightarrow1=\frac{10}{3}+b\Rightarrow\ldots \\ \ldots b=1-\frac{10}{3}=-\frac{7}{3} \end{gathered}$

Having found m and b, the final answer is

$y=\frac{2}{3}x-\frac{7}{3}$