All four quadrants
Explanation:
We have the following inequality:
[tex]y \leq \frac{2}{7}x+1[/tex]
So the first step we need to perform is to plot the line:
[tex]y = \frac{2}{7}x+1[/tex]
[tex]If \ x=0 \\ \\ y=\frac{2}{7}(0)+1 \\ \\ y=1 \\ \\ \\ If \ y=0: \\ \\ 0=\frac{2}{7}(x)+1 \\ \\ x=-\frac{7}{2}=-3.5[/tex]
So the line passes through the points:
[tex](0,1) \ and \ (-3.5,0)[/tex]
To find the shaded region, let us take a point, namely, the origin and test it in the inequality:
[tex]y \leq \frac{2}{7}x+1 \\ \\ 0\leq \frac{2}{7}(0)+1 \\ \\ 0\leq 1 \ True![/tex]
Since this is true, then the shaded region includes this point. This is shown below and as you can see the solutions exist in all four quadrants.
Learn more:
Inequalities: https://brainly.com/question/12890742
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