Question 928887
Line 1
{{{x}}}..|{{{y}}}
{{{-3}}}|{{{7}}}
{{{-2}}}|{{{5}}}

the slope-intercept form:

{{{y=mx+b}}}

the system in slope-intercept form:

{{{7=-3m+b}}}.....1
{{{5=-2m+b}}}.....2
_____________________subtract 2 from 1

{{{7-5=-3m-(-2m)+b-b}}}

{{{2=-3m+2m}}}

{{{2=-m}}}

{{{highlight(m=-2)}}}

go to 1 or 2, substitute {{{-2}}} for {{{m}}} and find {{{b}}}

{{{5=-2m+b}}}.....2

{{{5=-2(-2)+b}}}

{{{5=4+b}}}

{{{5-4=b}}}

{{{highlight(b=1)}}}

your equation is:

{{{y=-2x+1}}}


Line 2

{{{x}}}|	{{{y}}}
{{{0}}}|	{{{5}}}
{{{2}}}|	{{{1}}}

the system in slope-intercept form:

{{{5=m*0+b}}}.....1
{{{1=m*2+b}}}.....2
_____________________________

{{{5=b}}}.....1a.....so, {{{highlight(b=5)}}}
{{{1=m*2+b}}}.....2
_____________________substitute {{{5}}} for {{{b}}} from 1a in 2

{{{1=m*2+5}}}.....2

{{{1-5=2m}}}

{{{-4=2m}}}

{{{-4/2=m}}}

{{{highlight(m=-2)}}} ...line 1 and line 2 have same slope; until now we can say they are parallel


your equation is:

{{{y=-2x+5}}}


check them on a graph:


{{{drawing( 600, 600, -10, 10, -10, 10,circle(0,5,.12),locate(0,5,p(0,5)),circle(2,1,.12),locate(2,1,p(2,1)),circle(-2,5,.12),locate(-2,5,p(-2,5)), circle(-3,7,.12),locate(-3,7,p(-3,7)), graph( 600, 600, -10, 10, -10, 10, -2x+1, -2x+5)) }}}
 
Line 1: {{{y = -2x +1}}}   
Line 2: {{{y = -2x +5 }}}