Question 192871
<font face="Tahoma" size=1.5>
</pre><font size=4><b>
EQN1 : {{{4x - 6y = 12 }}}

Let us find the intercepts.
Let Fy=0:
{{{4x-6(0)=12}}}
{{{cross(4)x/cross(4)=cross(12)3/cross(4)1}}}
{{{red(x=3)}}}, X-Intercept
Let Fx=0:
{{{4(0)-6y=12}}}
{{{cross(-6)y/cross(-6)=cross(12)2/cross(-6)1}}}
{{{red(y=-2)}}}, Y-Intercept


Confirming to Slope-Intercept Form,{{{system(y=mx+b)}}}:
{{{4x-6y=12}}}
{{{4x-12=6y}}} ---> {{{(4x-12)/6=cross(6)y/cross(6)}}}
{{{y=(4/6)x-12/6}}}
{{{red(y=(2/3)x-2)}}}
We see graph,
{{{drawing(400,400,-7,7,-7,7,graph(400,400,-7,7,-7,7,(2/3)x-2),blue(circle(3,0,.12)),blue(circle(0,-2,.12)))}}} ----> The Line 4x-6y=12 passes thru point (3,0), X-Intercept and point (0,-2), Y-Intercept.



EQN 2 : {{{x - 5y = 10 }}}


Finding the Intercepts:
Let Fy=0:
{{{x-5(0)=10}}}
{{{red(x=10)}}}
Let Fx=0:
{{{0-5y=10}}}
{{{cross(-5)y/cross(-5)=cross(10)2/cross(-5)1}}}
{{{red(y=-2)}}}


Confirming to Slope-Intercept Form,{{{system(y=mx+b)}}}
{{{x-5y=10}}}
{{{x-10=5y}}}
{{{(x-10)/5=cross(5)y/cross(5)}}}
{{{red(y=(1/5)x-10/5=(1/5)x-2)}}}



We see graph,
{{{drawing(400,400,-5,15,-5,5,graph(400,400,-5,15,-5,5,(1/5)x-2),blue(circle(10,0,.16)),blue(circle(0,-2,.16)))}}} ----> Line x-5y=10 passes thru point (10,0),X-Intercept, and point (0,-2), Y-Intercept.



Thank you,
Jojo</font>