Question

Find the equation (in terms of x ) of the line through the points (-4,-4) and (2,4)

Answer 1

`y=(4)/(3)x+(4)/(3)`

Explanation:

Let
`(x_1,y_1)\rightarrow(-4,-4)` and
`(x_2,y_2)\rightarow(2,4)`:

Determine slope

`m=(y_2-y_1)/(x_2-x_1)\\ \\m=(4-(-4))/(2-(-4))\\ \\m=(4+4)/(2+4)\\ \\m=(8)/(6)\\ \\m=(4)/(3)`

Use either coordinate point to find "b", the y-intercept

`y=mx+b\\\\4=(4)/(3)(2)+b\\ \\4=(8)/(3)+b\\ \\(4)/(3)=b`

Final Equation

`y=(4)/(3)x+(4)/(3)`