What Is #y+3=7(x-2)# written in standard forma?

2 Answers
Jul 16, 2017

#7x-y = 17#

Explanation:

Standard form: #ax+by=c#
Note that #a#, #b#, and #c# are integers and #a# is positive.

#y+3=7(x)+7(-2) " "" "" "" "# (distributive property)

#y+3=7x-14 " "" "" "" "" "" "color(white)"-."# (simplify)

#y=7x-14-3 " "" "" "" "" "" "color(white)"-."# (isolate the #y#)

#y=7x-17 " "" "" "" "" "" "" "" "# (simplify)

#-7x + y = -17 " "" "" "" "" "" "# (move the #x# term)

#7x - y = 17 " "" "" "" "" "" "" "" "# (multiply by #-1#)

Jul 17, 2017

#y=7x-17larr# Slope intercept form

#7x-y=17 larr #Standard form

Explanation:

Consider the #color(blue)(7)color(green)((x-2))#

Multiply everything inside the brackets by 7

#color(green)([color(blue)(7xx) x] +[color(blue)(7xx)(-2)]#

#" "[7x] +" " [-14]#

#" "7x-14#
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Putting it all together

#y+3=7x-14#

Subtract #color(red)(3)# from both sides

#color(green)(y+3color(red)(-3)" "=" "7x-14color(red)(-3)#

#y+0=7x-17#

#y=7x-17larr# Slope intercept form
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#7x-y=17 larr #Standard form