Question

What is the equation of the line between `(-1,12)` and `(7,-7)`?

Answer 1

The equation of the line that passes through the points `A(-1,12)` and `B(7,-7)` is :
`y = - 19/8 x + 77/8`

Explanation:

The standard form of the equation of a line is `y = m x + p` with m the slope of the line.

STEP 1 : Let's find the slope of the line.
`m = (y_B - y_A)/(x_B - x_A) = (-7-12)/(7+1) = - 19/8`
N.B : The fact that the slope is negative indicates the line decreases.

STEP 2 : Let's find p (coordinate at origin).
Use the point-slope formula with one of our points, e.g. `A(-1,12)` and `m = - 19/8`.

`12 = - 19/8 * -1 + p`
`p = 77/8`

Cross-check: Check the equation with the second point.
Use `B(7,-7)` in the equation :
`y = - 19/8 * 7 + 77/8 = - 96/8 + 77/8 = -56/8 = -7`
-> Perfect !