Question

How do you write the equation in slope intercept form given (1,4) and (2,-5)?

Answer 1

`y=-9x+13`

Explanation:

Let's find the slope for `y=color(red)(m)x+b`, using `(y_2 - y_1)/(x_2 - x_1)`

`(-5 - 4)/(2 - 1)` gives us `-9/1` for `m`

Now we need to find `b`, which is the `y`-intercept. That means, the value of `y` when `x=0`

To find that, let's us the point-slope formula again:

`(y_2 - y_1)/(x_2 - x_1)` with `(0,?)` and `(1, 4)`

`(? - 4)/(0 - 1)`
Now what? Well, we already know what the slope is. It's `-9/1`. Now we can solve!

`(? - 4)/(0 - 1)=-9/1`

`(?-4)/-1=-9`

multiply by `-1` on both sides

`?-4=9`

add `4` on both sides

`?=13`

Now we have our `y`-intercept. It's `13`!

`y=-9x+13`

Let's graph our equation and make sure it goes through the points `(2, -5)` and `(1, 4)`:

graph{y=-9x+13}
It does! We were right

Answer 2

`y=-9x+13`

Explanation:

`"the equation of a line in "color(blue)"slope-intercept form"` is.

`color(red)(bar(ul(|color(white)(2/2)color(black)(y=mx+b)color(white)(2/2)|)))`
where m represents the slope and b. the y-intercept.

`"to calculate m use the "color(blue)"gradient formula"`

`color(red)(bar(ul(|color(white)(2/2)color(black)(m=(y_2-y_1)/(x_2-x_1))color(white)(2/2)|)))`
`(x_1,y_1),(x_2,y_2)" are 2 coordinate points"`

`"the points are " (x_1,y_1)=(1,4),(x_2,y_2)=(2,-5)`

`rArrm=(-5-4)/(2-1)=(-9)/1=-9`

`rArry=-9x+blarr" is the partial equation"`

`"to find b, substitute either of the 2 given points into"`
`"the partial equation"`

`"using " (1,4)`

`4=-9+brArrb=13`

`rArry=-9x+13larrcolor(red)" in slope-intercept form"`