Question

How do you write an equation with slope -2 that passes through the point (1, 5) ?

Answer 1

`(y-5)=(-2)(x-1)` (point-slope form), or
`y=-2x+7` `color(white)("XXXXXX")` (slope-intercept form), or
`2x+y=7` `color(white)("XXXXXXXX")` (standard form)

Explanation:

Point-slope form of a line with slope `m` through the point `(hatx,haty)` is
`color(white)("XXX")(y-haty)=m(x-hatx)`

For the given values:
`color(white)("XXX")(y-5)=(-2)(x-1)`

This can be converted to other forms:
`color(white)("XXX")`slope-intercept form: `y = mx+b`
`color(white)("XXXXXX")(y-5)=(-2)(x-1)`
`color(white)("XXXXXX")`becomes `y = -2x+7`
or
`color(white)("XXX")`standard form: `Ax+By=C`
`color(white)("XXXXXX")2x+y=7`

Answer 2

`y=-2x+7`

Explanation:

Use the formula `y-y_1=m(x-x_1)`

Your slope is `m`, so just subsitute `-2` into the equation, which gets you

`y-y_1=-2(x-x_1)`

Get your two points that you already have and substitute them into the equation, then expand the brackets to get your final answer.

`y-5=-2(x-1)`
`rArr` `y-5=-2x+2`
`rArr` `y=-2x+7`