Question 121541
The slope-intercept form is one way of doing it but I don't think it's as intuitive as finding the x and y intercepts. 
Let's do it a different way. 
Find the x-intercept of the graph.
Then find the y-intercept of the graph. 
{{{x-2y = 8}}} 
When y=0, then
{{{x-2(0)=8}}}
{{{x=8}}}

When x=0, then
{{{0-2y=8}}}
{{{y=-4}}}
Now you have two points on the graph (0,-4) and (8,0). 
It’s easier to graph this way than with a point and the slope, I think. 
First graph the two points. 
{{{drawing( 300, 300, -10, 10, -10, 10,grid( 1 ),circle( 0,-4, .3 ),circle(8,0,.3))}}}
Then draw the line containing the two points. 
{{{drawing( 300, 300, -10, 10, -10, 10,grid( 1 ),circle( 0,-4, .3 ),circle(8,0,.3),green(line( -12, -10, 20, 6)))}}}


{{{3x-2y=12}}} 
When y=0, then
{{{3x-2(0)=12}}}
{{{x=4}}}

When x=0, then
{{{3(0)-2y=12}}}
{{{y=6}}}
The two points on the graph are(4,0) and (0,6). 
Graph the two points. 
{{{drawing( 300, 300, -10, 10, -10, 10,grid( 1 ),circle( 4,0, .3 ),circle(0,6,.3))}}}
Then draw the line containing the two points. 
{{{drawing( 300, 300, -10, 10, -10, 10,grid( 1 ),circle( 4,0, .3 ),circle(0,6,.3),green(line( -12, 24, 12, -12)))}}}
You can then look at your graphs and find the slope by using change in y divided by change in x. 
{{{m[1]=1/2}}}
{{{m[2]=-3/2}}}