Question

Find the equation of the line through the pints (1,4) and (-2,-5)?

Answer 1

`y=3x+1`

Explanation:

I'm assuming this is a straight line in the form of `y=mx+b`.

We first find the gradient of the line, `m`. It is given by

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

It doesn't matter which one you choose for `y_1` or `y_2`, just remember that if you take `y_1` as the first `y` coordinate, which is `4` in this case, then `x_1` will also correspond to the first `x` coordinate, which is `1`.

So, we get:

`m=(-5-4)/(-2-1)`

`=(-9)/-3`

`=3`

So, the slope of the line is `3`.

Then, the line is `y=3x+b`.

Now, we just plug in the values of one of the coordinates.

We know that the line passes through `(1,4)`, so we plug in `x=1,y=4`, and we get

`4=3*1+b`

`4=3+b`

`b=1`

`:.` The line is `y=3x+1`.

If we plug in `(-2,-5)`, which is `x=-2,y=-5`, we get:

`-5=3*-2+1`

`-5=-6+1`

`-5=-5` (correct!)

Indeed, the line is then `y=3x+1`.

Here is a graph of the line:

graph{3x+1 [-5.49, 6.995, -1.75, 4.493]}