x+2y = 6
2y = -x + 6
y = -1/2 x +3
From this you can see that the y-intercept is at 3 (not 2 like you have it inyour sketch), and the slope is -1/2. You can also determine the x-intercept by setting y =0, and you see that the x-intercept is at x= 6.
I just edited my previous post to add a figure - maybe that will help.
Start by plotting the y-intercept, which in this case is -1. So plot the point (0,-1). Since the slope is -2, starting from the y-intercept count 2 units up (positive y direction) and 1 unit to the left (negative x direction). This puts you at the point (-1,1). Now draw a straight line through these 2 points. The only "trick" here is to remember that the definition of "slope" is "rise over run," which is a measure of how fast the line rises. A negative slope means the line rises up to the left, and a positive slope means it rises up to the right. As a check, you can calculate the x-intercept (the point onteh line where y = 0): 0 = -2x-1, so x =-1/2. Now see if the point (-1/2, 0) is on the line you just plotted - if it is, then life is good.
to correctly draw line do this let's say you have equation of the line as yours y=3x-1
you need just 2 points (any points) to draw the line
let's make "table"
let's say that x=0 . because of the equation y=3x-1 implies that y=3*0-1 = -1 . now you have one point M(x=0, y=-1) == M(0,-1) now we need one more let's say now that x=1 so put x=1 to equation and you get y=3*1-1 = 2 now you have second point N(1,2) just now connect those two lines and you have correctly drawn line
P.S. doesn't matter which value of x are you chose it could be x= 10 -> y= 3*10-1 = 29 and x=-10 -> y= 3*(-10)-1 = -31 and again you have two points M(10,29) N(-10,-31) and again just connect those two points and you will get the same line