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Answer
The graph of y ≤ -⅓ x + 1 is presented below.
The shaded region indicates the wanted region.
Explanation
2) y ≤ -⅓ x + 1
When plotting the graph of linear inequality equations, the first step is to first plot the graph of the straight line normally, using intercepts to generate two points on the linear graph.
If the inequality sign is (< or >), then the line drawn will be a broken line.
If the inequality sign is (≤ or ≥), then the line drawn is an unbroken one.
The shaded region now depends on whether the inequality sign is facing y or not.
If the inequality sign is facing y, it means numbers above the line plotted are the wanted region and the upper part of the graph is shaded.
If the inequality sign is not facing y, it means numbers below the line plotted are the wanted region and the lower part of the graph is shaded.
So, for the normal line of y = -⅓ x + 1, we will use intercepts to obtain two points on this line.
y = -⅓ x + 1
when x = 0,
y = -⅓ x + 1
y = -⅓ (0) + 1
y = 0 + 1
y = 1
First point on the line is (0, 1)
y = -⅓ x + 1
when y = 0,
y = -⅓ x + 1
0 = -⅓ x + 1
⅓ x = 1
Multiply both sides by 3
x = 3
Second point on the line is (3, 0)
The inequality sign is ≤, so, the line will be an unbroken line.
Then, for the shaded region, it will be the area under the line.
The graph will be presented under 'Answer' above.
Hope this Helps!!!
