Question 17311
finding the coordinates of two points does not require solving the equation at all. The two easiest points to find are the x- and y-intercepts. 
The x-intercept occurs when y = 0. 
The y-intercept occurs when x = 0. 
Substitute 0 for y: 
3x - 6(0) = 9 
3x = 9 
x = 3 
The x-intercept is at the point (3, 0). 
Substitute 0 for x: 
3(0) - 6y = 9 
-6y = 9 
y = -9/6 
y = -3/2 
The y-intercept is at the point (0, -3/2). 
To solve the equation for x means that we want to isolate the variable x on one side of the equals sign and move everything else to the other side. 
Start by isolating 3x first; move the -6y term to the other side by adding it to both sides of the equation. 
3x - 6y + 6y = 9 + 6y 
3x = 9 + 6y 
Now we solve for x by dividing both sides by 3. 
(3x)/3 = (9 + 6y)/3 
x = 9/3 + (6y)/3 
x = 3 + 2y 
We do something similar to solve the equation for y. 
Move the 3x term to the other side to isolate -6y. We do this by subtracting 3x from both sides. 
3x - 3x - 6y = 9 - 3x 
-6y = 9 - 3x 
Divide both sides by -6 to solve for y. 
(-6y)/(-6) = (9 - 3x)/(-6) 
y = 9/(-6) - (3x)/(-6) 
y = -3/2 + x/2 
This last equation is usually written like this: 
y = (1/2)*x - 3/2 
and it is called the slope-intercept form of the equation for the line. It is called this because it shows at a quick glance what the slope is and what the y-intercept is. 
It's this form: y = m*x + b 
where m is the slope and b is the y-intercept. 
y = (1/2)*x - 3/2 
Solving the equation for y shows us that m = 1/2 and b = -3/2.