First, you want to isolate y to get this thing in y=mx+b form.
x-y=-3
Subtract x from each side
-y=-x-3
Divide both sides by -1
y=x+3
Now you have your equation for the line in y=mx+b form. m=slope, and b=y-intercept. Therefore, your slope here is 1 (since x is the same as 1x), and your y-intercept is 3.
Now to graph it, there are many different ways. I'll show you two ways to do it:
1) Take the equation y=x+3 and plug in a value for x. Any value. Say 3.
y=3+3
y=6
So one point to plot is (3,6).
Now plug in another random number, like 2.
y=2+3
y=5
(2,5)
Now how about -1?
y=-1+3
y=2
(-1,2)
And one point you already know is (0,3) because of the y intercept.
Now plot the points and draw a line through all four of them:
Equation describes a sloping line. For any
equation ax+by+c = 0, slope is .
X intercept is found by setting y to 0: ax+by=c becomes ax=c. that means that x = c/a. -3/1 = -3.
Y intercept is found by setting x to 0: the equation becomes by=c, and therefore y = c/b. Y intercept is -3/-1 = 3.
Slope is -1/-1 = 1.
Equation in slope-intercept form: y=1*x+3.
Now the next way I'm going to show you, in my opinion, is an over-complicated brain fart. But I will show it to you anyway, just in case it will be easier for you to do it this way (maybe).
2)Look at the equation y=x+3.
Your slope=the change in y/change in x. In other words, in this case, 1/1. Your y-intercept is 3.
Start at the point (0,3).
Since the change in y is 1, move up one.
Since the change in x is 1, move to the right one.
(Does this feel like a board game yet?)
Now plot the point.
Repeat the process.
Now go back to (0,3). Since your slope can also be considered -1/-1, your change in y can be -1. So move down one.
Same applies to your change in x. It can be -1. So move to the left 1.
Plot the point.
Repeat the process.
Draw a line through the points. (Now we're doing a Connect-the-dots)