Question

How do you write the point slope form of the equation given (-5,5) and (0,2)?

Answer 1

`y = -3/5x + 2`

Explanation:

The point-slope form formula is:
`y - y_1 = m(x - x_1)`

First me need to find `m`, the slope. We do this by using the slope formula which is:
`m = (y_2 - y_1)/ (x_2 - x_1)`

Now we plug in our points:
`(x_1 = -5, x_2 = 0, y_1 = 5, and y_2 = 2)`

`m = (2-5)/(0-(-5)`

When we simplify we get our slope, which is:
`m = -3/5`

To find `y_1` and `x_1,` we can use the original points we were given.
I'm going to use `y_1 = 2` and `x_1 = 0`. (You can use `y_1 = -5` and `x = 5` if you want, the final answer will be the same.)

Now we plug all of this information into the point-slope formula
`y - 2 = -3/5(x-0)`

We combine like terms on the left side and distribute `-3/5` into the parenthesis (`-3/5` multiplied with `x` and `0`).

`y - 2 = -3/5x + 0`

Now we isolate the `y` by adding 2 to both sides.

`y -2 + 2 = -3/5x + 2`

When we simplify we get:
`y = -3/5x + 2`