Question 834001
{{{2y=4x+6}}}
{{{2y/2=(4x+6)/2}}}
{{{highlight(y=2x+3)}}}
That's the slope-intercept form showing that
the intercept with the y-axis is at point (0,3),
and the slope is {{{2}}} . meaning that as {{{x}}} increases by {{{1}}} , {{{y}}} increases by {{{2}}} ,
from (0,3) to (1,5), and then to (2,7).
{{{drawing(300,300,-5,5,-2,8,
grid(1),red(line(-5,-7,5,13)),
red(circle(0,3,0.2)),green(circle(1,5,0.2)),
green(circle(2,7,0.2))
)}}}
 
{{{3y+2x=12}}}
{{{3y=-2x+12}}}
{{{3y/3=(-2x+12)/3}}}
{{{y=(-2/3)x+12/4}}}
{{{highlight(y=(-2/3)x+3)}}}
The intercept with the y-axis is at point (0,3),
and the slope is {{{-2/3}}} , meaning that the increases of {{{y}}} and {{{x}}} are in the ratio of {{{-2/3}}} .
That means that as {{{x}}} increases by {{{3}}} , {{{y}}} decreases by {{{2}}} ,
from (0,3) to (3,1), and then to (6,-1).
{{{drawing(300,300,-2,8,-2,8,
grid(1),red(line(-6,7,9,-3)),
red(circle(0,3,0.2)),green(circle(3,1,0.2)),
green(circle(6,-1,0.2))
)}}}