Question

How do you write an equation in standard form for a line passing through (–1, 2) and (3, 4)?

Answer 1

First find the slope of the line. This is (change in `y`) / (change in `x`).

For your example:

slope `= (Delta y)/(Delta x) = (4 - 2)/(3 - (-1)) = 2 / 4 = 1/2`

Slope intercept form is `y = mx + c` where `m` is the slope and `c` the intercept.

To calculate `c` we can subtract `mx` from both sides to get:

`c = y - mx`.

We know `m=1/2` and we have two example points that satisfy the equation of the line we're aiming for. Let us use `(-1, 2)`...

`c = y - mx = 2 - (1/2*-1) = 2+1/2 = 5/2`

So the equation of our line is:

`y = 1/2x + 5/2`