graph y=-x+6 in a coordinate plane
graph y=-x+6 in a coordinate plane
This is a linear equation in slope intercept form: y = m*x+b First note that -x is the same as -1*x. Thus your equation is the same as the equation y = -1*x+6.
To graph a line y = mx+b you first note that the line will contain the point (0,b) which is a y-intercept. Find another point by using the fact that the slope is the rise over the run. For example if the run is 1, then the rise will be m, while for a run of 4, the rise would be 4m etc.
For a second point we can choose any point of the form (run,b+rise) (move "run" units right and "rise" units up from y-intercept).
In your case the y-intercept is (0,6). Since m=-1 so that rise = -run, the other point could be (1,5) or (2,4), or any other point (n,6-n). Then just draw a straight line through the two points, which can be done with a ruler.
Since two points determine a line, you only need to find any two points on the line.
Method I:
Starting at y-int = 6, going up 1 unit and left 1 unit gives you another point. Drawing a line throught the two points, you have the graph.
Method II:
y-int = x-int = 6. Drawing a line throught the two points, you have the graph.