Question

A line passes through (-9,-5) and (2,-4)

Answer 1

The point-slope form of a line:

$y-y_1=m(x-x_1)\\\\m=\dfrac{y_2-y_1}{x_2-x_1}$

We have the points (-9, -5) and (2, -4). Substitute:

$m=\dfrac{-4-(-5)}{2-(-9)}=\dfrac{1}{11}\\\\y-(-5)=\dfrac{1}{11}(x-(-9))\\\\\boxed{y+5=\dfrac{1}{11}(x+9)}\leftarrow\boxed{\text{point-slope form}}$

The standard form of a line:

$Ax+By=C$

$y+5=\dfrac{1}{11}(x+9)$                multiply both sides by 11

$11y+55=1(x+9)$

$11y+55=x+9$     subtract 9 from both sides

$11y+46=x$      subtract 11y from both sides

$46=x-11y$

$\boxed{x-11y=46}\leftarrow\boxed{\text{standard form}}$