Question

Question #a77d0

Answer 1

First off, calculate the slope of the line using `{y_2-y_1}/{x_2-x_1}`

Explanation:

once you calculate the slope, `{-4--2}/{5-6}`= `{-2}/-1=2`

You can then plug that into the point-slope form

`y-y_1=m(x-x_1)`

You can pick either one of your points to use for `x_1 and y_1` because the line will go through both points

Answer 2

The way to solve this question is to first find the slope using the two points given and then use that slope like you would in point slope form.

The Final equation : `y + 2 = 2x - 12`

Explanation:

How to find slope given two points?
we know that slope is nothing but rise over run. That is the changed value in the `y` direction divided by changed value in the `x` direction.

Let the given points be `P_1(x_1,y_1)` and `P_2(x_2,y_2)`.
Suppose you subtract the `y's` of `P_2 & P_1` , what do you get?
you get the value of how much `y` has changed going from `P_1` to `P_2`. So you got the value of 'rise'
Now to the same thing with the `x's` of `P_2 and P_1` .you will get the value of run.

I have assumed that `P_1` is `(6,-2)` and `P_2` is `(5,-4)`. You can always assume the other way too.

slope = change in y/ change in x
= `(y_2 - y_1)/(x_2 - x_1)`
`=(-4 - (-2))/(5 - 6)` = `-2/-1` = `2`.
The slope is `2`. What next? plug the slope in the equation.

`y - y_1 = (slope) * (x - x_1)`
`y + 2 = 2 * (x - 6)` => `y + 2 = 2x - 12`.

You may use the `x_2 , y_2` values in the above equation instead of `x_1,y_1` as both points lie on the same line and hence are the solutions of the line equation