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

2 Answers
Alan P.
Oct 3, 2015

#(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#

zoe
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)#
#rArr##y-5=-2x+2#
#rArr# #y=-2x+7#

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