Question

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

Write the equation for line in point slope form and rewrite the equation in standard form using integers

Answer 1

The point-slope form of a line:

`y-y_1=m(x-x_1)\\\\m=(y_2-y_1)/(x_2-x_1)`

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

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

The standard form of a line:

`Ax+By=C`

`y+5=(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}}`