Question 215197
The equation of the line that goes through the point ( 2 ,8 ) and is parallel to the line 3 x + 3 y = 4 can be written in the form y = mx+b 


Step 1.  Let's rewrite 3x+3y=4 in slope-intercept form given as y=mx+b where m is the slope and b is the y-intercept.


{{{3x+3y=4}}}


{{{3x+3y-3x=-3x+4}}}


{{{3y=-3x+4}}}


{{{3y/3=-3x/3+4/3}}}


{{{y=-x+4/3}}}  slope-intercept form where {{{m=-1}}} and {{{b=4/3}}}


Step 2.  A parallel line to the one in Step 1 has the same slope or m=-1 for our example.  This line needs to pass through (2,8) or x=2 and y=8.  So we can use this to find b or the y-intercept.


{{{y=-x+b}}}


{{{8=-2+b}}}


{{{8+2=-2+b+2}}}


{{{10=b}}}


{{{b=10}}}


Step 3.  Our equation for the line is y=-x+10.


Here's the graph of the above situation;


{{{graph(400,400, -15,15,-15,15, -x+4/3, -x+10)}}}