Question 192766
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Given Line Eqns,{{{system( 8x - 4y = 12 (red(EQN1)), -4x + 2y = -6(red(EQN2)))}}}


We will get the intercepts for each line.
In {{{red(EQN1)}}}, Let Fy=0:
{{{8x - 4(0) = 12 }}}
{{{cross(8)x/cross(8)=cross(12)3/cross(8)2}}}
{{{red(x=3/2)}}}, X-Intercept
Let Fx=0:
{{{8(0)-4y=12}}}
{{{cross(-4)y/cross(-4)=cross(12)3/cross(-4)1}}}
{{{red(y=-3)}}}, Y-Intercept


Confirming to Slope-intercept Form,{{{system(y=mx+b)}}}
{{{8x - 4y = 12 }}}
{{{8x-12=4y}}} ----> {{{(8x-12)/4=cross(4)y/cross(4)}}}
{{{y=(8/4)x-12/4}}}
{{{red(y=2x-3)}}}

We'll see graph,
{{{drawing(400,400,-8,8,-8,8,graph(400,400,-8,8,-8,8,2x-3),blue(circle(3/2,0,.12)),blue(circle(0,-3,.12)))}}} ----> The line passes thru point (3/2,0) X-Intercept, and point (0,-3) Y-Intercept.




In {{{red(EQN2)}}}, let Fy=0:
{{{-4x + 2(0) = -6}}}
{{{cross(-4)x/cross(-4)=(cross(-6)-3)/(cross(-4)-2)}}}
{{{red(x=3/2)}}}, X-Intercept
Let Fx=0:
{{{-4(0)+2y=-6}}}
{{{cross(2)y/cross(2)=(cross(-6)-3)/(cross(2)1)}}}
{{{red(y=-3)}}}, Y-Intercept


Confirming to Slope-Intercept Form,{{{system(y=mx+b)}}}
{{{-4x + 2y = -6}}}
{{{2y=4x-6}}} ----> {{{cross(2)y/cross(2)=(4x-6)/2=(4/2)x-6/2}}}
{{{red(y=2x-3)}}} ---> <font color=blue>The Same as Line as above.</font>



Thank you,
Jojo</font>