Question

What is the slope and intercept of `y-(-4)=-1(x-6)`?

Answer 1

Slope: -1

x-intercept: (2, 0)

y-intercept: (0, 2)

Explanation:

`y - (-4) = -1(x-6)`

We know that the equation is in point-slope form:

Therefore, we know that the slope is `-1`.

To find the `x`-intercept, plug in `0` for `y` and solve for `x`:
`0 - (-4) = -1(x-6)`

`4 = -x + 6`

`-2 = -x`

`x = 2`

The `x`-intercept is at `(2, 0)`.

To find the `y`-intercept, plug in `0` for `x` and solve for `y`:
`y - (-4) = -1(0-6)`

`y + 4 = -1(-6)`

`y + 4 = 6`

`y = 2`

The `y`-intercept is at `(0, 2)`.

Hope this helps!

Answer 2

Slope `-1`, `x`-int `2` and `y`-int `2`

Explanation:

Our equation is in point-slope form

`y-y_1=m(x-x_1)`, where slope `m` and points (`x_1,y_1`).

We immediately see that our slope is `-1`. We can find the `y`-intercept by converting this to slope intercept form

`y=mx+b`, with slope `m` and a `y`-intercept of `b`.

Our equation simplifies to

`y+4=-1(x-6)`

We can distribute the negative on the right to get

`y+4=-x+6`

Lastly, we can subtract `4` from both sides to get

`y=-x+2`

We see that our `y`-intercept is `2`. What about the `x`-intercept? This can easily be found by setting `y` equal to zero.

`-x+2=0=>-x=-2=>x=2`

Therefore, our slope is `-1`, our `y`-intercept is `2`, and so is our `x`-intercept.

Hope this helps!