Question 112035
SOLUTIONS OF LINE {{{A }}}(3,3) (5,)(15,15) (34,34)(678,678) (1234,1234)
SOLUTIONS OF LINE {{{B}}} are: (3,-3) (5,-5) (15,-15)(34,-34)(678,-678) (1234,-1234)

a. form the equations of both line

We need {{{two}}}{{{ points}}} to find equation of line:


Line {{{A}}}

to find equation of form {{{y= mx + b}}}, where {{{m}}} is slope, and {{{b}}} is intercept, which passes through points ({{{x[1]}}}, {{{y[1]}}}) = ({{{3}}}, {{{3}}}) and ({{{x[2]}}}, {{{y[2]}}}) = ({{{15}}}, {{{15}}}), we need to calculate a slope {{{m}}}

Slope {{{m}}} is: 

{{{ m = (y[2] - y[1])/(x[2] - x[1]) }}},  

{{{ m = (15 - 3)/(15 - 3) }}},  

{{{m = 12/12}}}

{{{m = 1}}}



Intercept is found from equation:

{{{mx[1] + b = y[1]}}}……move {{{mx[1]}}}to the right  

{{{ b = y[1] - mx[1]}}}  

{{{ b = 3 - 1*3}}}  

{{{ b = 3 - 3}}}  


{{{ b = 0 }}}  

Then, your equation is:
{{{y=(1)x + (0)}}}

or

{{{y =  x }}}


Line {{{B}}}

to find equation of form y=ax+b, where a is slope, and b is intercept, which passes through points (x1, y1) = (3, -3) and (x2, y2) = (5, -5), we need to calculate a slope {{{m}}}

Slope {{{m}}} is: 

{{{ m = (y[2] - y[1])/(x[2] - x[1]) }}},  

{{{ m = (-5 - (-3))/(5 - 3) }}},  

{{{m = (-5 + 3)/2}}}

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

{{{m = - 1}}}



Intercept is found from equation:

{{{mx[1] + b = y[1]}}}……move {{{mx[1]}}}to the right  

{{{ b = y[1] - mx[1] }}}  

{{{ b = -3 - (-1*3) }}}  

{{{ b = -3 - (-3) }}}  

{{{ b = -3 + 3 }}}  

{{{ b = 0 }}}  

Then, your equation is:

{{{y=(-1)x + (0)}}}

or

{{{y = - x }}}



b. the co-ordinates of {{{the}}}{{{ point }}}{{{of }}}{{{intersection}}} of lines {{{a}}} and {{{b}}}
are : ({{{0}}},{{{0}}})


c. the co-ordinates of the intersections of lines {{{a}}} and {{{b}}} with the {{{x-axis}}} are ({{{0}}},{{{0}}})


d. the co-ordinates of the intersection of lines{{{ a}}} and {{{b}}} with the {{{y-axis}}} are ({{{0}}},{{{0}}})


*[invoke solve_by_graphing 1, 1, 0, -1, 1, 0]