Question 758418
Plot the points A({{{-6}}},{{{7}}}), B({{{2}}},{{{-3}}}), C({{{0}}},{{{8}}}), and D({{{-3}}},{{{-1}}}). 


{{{drawing( 600, 600, -10, 10, -10, 10,circle(-6,7,0.1),locate(-3,-1,D(-3,-1)),locate(0.3,8,C(0,8)),locate(2,-3,B(2,-3)),locate(-6,7,A(-6,7)),circle(-3,-1,0.1),circle(0,8,0.1),circle(2,-3,0.1), graph( 600, 600, -10, 10, -10, 10,0)) }}}

now find equations of  the lines passing through {{{AB}}} and {{{CD}}} and draw them:

 *[invoke change_this_name10094 -6, 7, 2, -3]

*[invoke change_this_name10094 0, 8, -3, -1]

now we can go back and put these lines on a graph above

{{{drawing( 600, 600, -10, 10, -10, 10,circle(-6,7,0.1),locate(-3,-1,D(-3,-1)),locate(0.3,8,C(0,8)),locate(2,-3,B(2,-3)),locate(-6,7,A(-6,7)),circle(-3,-1,0.1),circle(0,8,0.1),circle(2,-3,0.1), graph( 600, 600, -10, 10, -10, 10,3x+8,-1.25x-0.5)) }}}


as you can see from a graph, the point of intersection of {{{AB}}} and {{{CD}}} is ({{{-2}}},{{{2}}})


we can check it if we plug in {{{x=-2}}} and {{{y=2}}} in {{{y=3x+8}}} and {{{y=-1.25x-0.5}}}

{{{2=3(-2)+8}}}
{{{2=-6+8}}}
{{{2=2}}}......true

{{{2=-1.25(-2)-0.5}}}
{{{2=2.5-0.5}}}
{{{2=2}}}......true