Question 182500
</pre><font size=4><b>
{{{y-(2/3)x=-1/2}}}
It follows Slope-Intercept Form {{{system(y=mx+b)}}}--->{{{y=(2/3)x-(1/2)}}}
where{{{system(m=Slope=Rise/Run=2/3,b=YIntercept=-1/2)}}}
We see the graph:
{{{drawing(300,300,-5,5,-5,5,grid(1),graph(300,300,-5,5,-5,5),circle(0,-1/2,.12),green(locate(1/4,-1/2,yIntercept)))}}}
Now, having {{{Slope=m=2/3}}}, means "Rise" on the Y-Axis of "2"--->UP or DOWN in the increment of "2" from the Y-Intercept.
From {{{-1/2}}}, UP by "2" is "1-1/2=1.50" right?
Next, "RUN" means on the X -Axis of increment of "3".
From {{{-1/2}}}, since it's Y-Intercept, {{{x=0}}} and follows point (0,-1/2)right? So "RUN" meaning to the left or right of the X-Axis and we'll go the right first. So from "0" moving "3", X-intercept will be "3".
So our first point from the Y-Intrecept is (x,y)=(3,1.5)
.
Next, again 3 steps to the right of X-axis= {{{3+3=highlight(6)}}}
Also, 2 steps Up of the Y-Axis={{{1.5+2=highlight(3.5)}}}
Next point,-------> (6,3.5)
.
Next, again 3 steps on the X-axis={{{6+3=highlight(9)}}}
Also, 2 steps Up on the Y-Axis={{{3.5+2=highlight(5.5)}}}
Next point,-----------> (9,5.5)
.
We now go the "Left" and "Down" from the Y-Interecept.
From "0" to the left of 3 steps={{{highlight(-3)}}}
From "-1/2" down 2={{{highlight(-2.5)}}}
So our point will be --------> (-3,-2.5)
Next, 3 more steps to the left={{{-3+-3=highlight(-6)}}}
Also, 2 steps more down={{{-2.5+-2=highlight(-4.5)}}}
Point will be ,---------> (-6,-4,5)
Again, 3 more steps ot the left={{{-6+-3=highlight(-9)}}}
Also, 2 more steps down={{{-4.5+-2=highlight(-6.5)}}}
Point will be,---------> (-9,-6.5)
Now we plot all Points:
{{{drawing(400,400,-10,10,-10,10,grid(1),graph(-10,10,-10,10,(2/3)x-1/2),circle(0,-1/2,.15),green(circle(3,1.5,.15)),green(circle(6,3.5,.15)),green(circle(9,5.5,.15)),green(circle(-3,-2.5,.15)),green(circle(-6,-4.5,.15)),green(circle(-9,-6.5,.15)))}}}---->{{{drawing(400,400,-10,10,-10,10,grid(1),graph(400,400,-10,10,-10,10,(2/3)x-1/2),circle(0,-1/2,.15),green(circle(3,1.5,.15)),green(circle(6,3.5,.15)),green(circle(9,5.5,.15)),green(circle(-3,-2.5,.15)),green(circle(-6,-4.5,.15)),green(circle(-9,-6.5,.15)))}}}
Thank you,
Jojo</pre>