identify the graph of the solution set for the inequality X-2y<2
To graph the solution set for the inequality X - 2y < 2, we first need to re-arrange the equation in slope-intercept form (y = mx + b).
Let's isolate y:
-2y < -x + 2
Dividing by -2:
y > (1/2)x - 1
Now let's plot this line.
1. Start by plotting the y-intercept (0, -1).
2. Use the slope (m = 1/2) to find additional points. Since the slope is positive, we move up 1 unit and right 2 units from the current point. Plot (2, 0) and connect these two points with a line.
However, since the inequality is y > (1/2)x - 1 (not including the line itself), we need to use a dashed line instead of a solid line.
Since y > (1/2)x - 1, the graph falls above the line and extends infinitely in that direction.
Therefore, the graph for the solution set of this inequality is a dashed line that slants upward and to the right, with shading above the line.