Question 191071
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1) 4x – 2y = 12 -----> to Slope-Intercept Form ,{{{system(y=mx+b)}}}



Move "y" to the right and the constant 12 to the left: (change signs)
{{{4x-12=2y}}} ---> {{{(4x-12)/2=cross(2)y/cross(2)}}}
{{{y=(4/2)x-12/2}}}, reduceed to:
{{{red(y=2x-6)}}}


* Above Eqn has y-Interecept of (0,-6) and slope of 2.
{{{drawing(300,300,-4,4,-10,6,grid(1),graph(300,300,-4,4,-10,6,2x-6),blue(circle(0,-6,.08)),green(circle(2,-2,.08)),green(circle(1,-4,.08)),green(circle(-1,-8,.08)))}}}



2) Verify that the ordered pair (3, -3) is a solution to the equation 
3x + 4y = -3


Let fy=0:
{{{3x+4(0)=-3}}}
{{{3x=-3}}} ----> {{{cross(3)x/cross(3)=cross(-3)1/cross(3)1}}}
{{{red(x=-1)}}}, X-Intercept


Let fx=o:
{{{3(0)+4y=3}}}
{{{4y=-3}}} ----> {{{cross(4)y/cross(4)=-3/4}}}
{{{red(y=-3/4)}}}, Y-Intercept




Via Slope-Intercept Form,{{{system(y-mx+b)}}}


{{{4y=-3-3x}}} ----> {{{cross(4)y/cross(4)=(-3-3x)/4}}}
{{{y=(-3/4)x-3/4}}}

We see the graph:
{{{drawing(300,300,-5,5,-5,5,grid(1),graph(300,300,-5,5,-5,5),blue(circle(-1,0,.10)),blue(circle(0,-.75,.10)))}}} ---->{{{drawing(300,300,-5,5,-5,5,grid(1),graph(300,300,-5,5,-5,5,-(3/4)x-3/4),blue(circle(-1,0,.10)),blue(circle(0,-.75,.10)),green(circle(3,-3,.12)))}}}


*The Line passing thru point (3,-3)


Subst. to the Eqn:
{{{3x + 4y = -3}}}
{{{3(highlight(3))+4(highlight(-3))=-3}}}
{{{9-12=-3}}}
{{{-3=-3}}}, Point (3,-3) is a solution 



Thank you,
Jojo</font>