Step-by-step explanation:
x + y ≤ 6
You'll have to express the linear inequality into an equality statement (in slope-intercept form, y = mx + b) in order to graph. You'll have to use a solid line because of the "≤ " symbol.
y = - x + 6
Next, you'll have to choose two points to use for graphing. It's always safe to start with the y-intercept, (0, 6).
From there, you could use the slope (m = -1) and do the "rise over run" technique to plot your next point. Going up 1, left 1 will get you to (-1, 7); going down 1 right 1 will get you to point (1, 5). Connect your points and create a straight line.
Next, to determine which region to shade, you must choose a convenient test point (that's not on the line) to see whether the given test point will satisfy the inequality statement.
Let's choose the point of origin, (0, 0), and plug its values into the inequality statement:
x + y ≤ 6
0 + 0 ≤ 6
0 ≤ 6 (True statement). This means that you should shade the half-plane region where the test point is located (left side of the plane).
The first screenshot shows how I created the lines by plotting the first three points. The second screenshot shows the actual graph with the shaded region.
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