What is the equation of the line with slope # m= 1# that passes through # (7,13) #?

2 Answers
Jan 21, 2016

#(y-13)=1(x-7)# in explicit slope-point form
or
#x-y=-6# in standard form

Explanation:

General slope-point form is
#color(white)("XXX")(y-bary)=m(x-barx)#
for a line with slope #m# through the point #(barx,bary)#

Substituting the given values results in
#color(white)("XXX")y-13=1(x-7)#

To convert to standard form: #Ax+By=C#
#color(white)("XXX")-x+y-13=-7#

#color(white)("XXX")-x+y=6#

#color(white)("XXX")x-y=-6#

or, in explicit standard form:
#color(white)("XXX")1x-1y=-6#

Jan 22, 2016

A different approach to solving this one!

#y=x+6#

Explained with a lot of detail!

Explanation:

#color(blue)("Assumption "-> " this is a strait line graph")#

Standard equation form for a strait line graph:

#y=mx+c#.....................(1)

Given: slop (gradient) #->m=1#

so equation (1) becomes:

#y=(1)x+c#

But #1xx x =x#

#y=x+c#........................(2)

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
#color(blue)("To find the value of "c)#
Using given point of #x=7 and y=13#

Equation (2) becomes:

#y=x+c color(white)(..x.)->color(white)(.x..)13=7+c#

#color(blue)(c=13-7= 6)# as predicted.
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

#y=x+6#