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

2 Answers
Oct 3, 2015

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

Oct 3, 2015

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)
rArry-5=-2x+2
rArr y=-2x+7