Question 63532
If the line containing the points (-8,m) and (2,1) is parallel to the line containing the points (11,-1) and (7,m+1), what is the value of m?
:
We know that the slope = (y2-y1)/(x2-x) and parallel lines have equal slopes:
Slope 1 = Slope 2
 {{{(1-m)/(2-(-8))}}} = {{{((m+1)-(-1))/(7-11)}}}
:
{{{(1-m)/(2+8)}}} = {{{(m+1 + 1)/(7-11)}}}
:
{{{(1-m)/10}}} = {{{(m+2)/(-4)}}}
:
Cross multiply and solve for m:
10(m+2) = -4(1-m)
10m + 20 = -4 + 4m
10m -4m = -4 - 20
6m = - 24
m =-24/6
m = -4
:
:
Check to see if they have the same slopes, substitute -4 for m
{{{(1-m)/(2-(-8))}}} = {{{((m+1)-(-1))/(7-11)}}}
:
{{{(1-(-4))/(2-(-8))}}} = {{{((-4+1)-(-1))/(7-11)}}}
:
{{{(+5)/(+10)}}} = {{{((-3)+ 1)/(-4)}}}
:
{{{(+5)/(+10)}}} = {{{(-2)/(-4)}}}
;
Both slopes are +(1/2)
:
Make sense to you?