Question 397332
given:

{{{x1= 7}}}
{{{ y1= 10}}}
{{{ x2= 4 }}}
{{{y2= 2}}}

solpe {{{m= (y2-y1)/(x2-x1)}}}

= {{{(2-(10))/(4-(7))}}}

= {{{(2-10)/(4-7)}}}

= {{{-8/-3}}} 

={{{8/3}}}


{{{b = (y1-m*x1)}}}


{{{b =10-((-8)/(-3))(7) = 10- (56/3) = -26/3}}}

Equation: {{{y= mx +b }}}, {{{m = slope}}}

Equation of the line is :


 {{{y = (8/3) x -26/3}}} ----(1)



To find the {{{intersection}}} of this line with {{{y=x}}}, replace{{{ y}}} with {{{x}}} in (1)

{{{x = (8/3)x - 26/3}}}


{{{3x=8x-26}}}


{{{-5x=-26}}}


{{{x=26/5}}}


{{{y=(8/3)(26/5)-26/3}}}


{{{y=208/15 -26/3}}}


{{{y=78/15 = 26/5=5(1/5)}}}


{{{A=5(1/5)}}}


{{{B=5(1/5)}}}


graph:

in standard form you have:

{{{(8/3) x - y = 26/3 }}}

{{{y=x}}}...or {{{x-y=0}}}


*[invoke solve_by_graphing "(8/3)", -1, "(26/3)", 1, -1, 0]