Question

What is the equation of the line through points (-2, -1) and (2, -6)?

Answer 1

`y = -5/4(x) -7/2`

Explanation:

Given `A(x_1, y_1) and B(x_2, y_2)`. The gradient of a line is given by `(Deltay)/(Deltax)` which is usually donated by `m`.
So, `m = (Deltay)/(Deltax) = (y_2 - y_1)/(x_2 - x_1)`

`m = (y_2 - y_1)/(x_2 - x_1)`

`m = (-6- (-1))/(2 -(-2))`

`m = -5/4`

Now generally line equation is written in the form `y=mx+c`.
From above any of the 2 coordinates can be taken into consideration,
Hence,
`-6 = -5/4 (2) + c`

`-6 + 5/2 = c`

Our y-intercept is `-7/2`

Therefore our equation is
`y = -5/4(x) -7/2`