`y=-1/3x +1` is a linear equation. Hence, its graph is a line.
Also, the given equation is in slope-intercept form y=mx+b where m is the slope and b is the y-intercept.
So, the slope of the line is `-1/3` and its y-intercept is (0,1).
To graph, start with the point (0,1). Then, use the slope to determine the other points.
Since the slope is negative, one the points is 1 unit down and 3 units to the right of y-intercept. This is point (3, 0). From here, move 1 unit down and 3 units to the right again. The other point then is (6, -1).
Also, the points above the y-intercept can be determined by moving 1 unit up and 3 units to the left. So, one of the points is (-3, 2). Repeating the steps, the other point is (-6, 3).
Now that some of the points of y=-1/3x+1 are known, connect them. And extend the line on both ends.
Hence, the graph of `y=-1/3x+1` is :