Question

How do you write and equation of a line given (10, –2) with a slope of –1?

Answer 1

`y=-x+8` or graph{y=-x+8 [-22.8, 22.83, -11.4, 11.4]}

Explanation:

The equation of a line is `y=mx+b`.

Since we know that `m=-1` (`m` is the slope), the equation will be `y=(-1)x+b`

Put in (10, -2) as `x=10` and `y=-2`:

`-2=(-1)*10+b->`
`-2=-10+b->` (Multiply `-1` and `10`)
`8=b` (Add `10` to both sides)
Flip equation: `b=8` (Switch sides)

Whole equation: `y=-x+8`

`-x` because `-1*x=-x`

Ans: `y=-x+8`

Hopefully I'm right ;/

Answer 2

`y=-x+8`

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 is the slope and b the y-intercept"`

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

`"to find b substitute "(10,-2)" into the partial equation"`

`-2=-10+brArrb=8`

`rArry=-x+8larrcolor(red)" in slope-intercept form"`
graph{-x+8 [-10, 10, -5, 5]}