Answer: C.
Explanation
Given
[tex]y-x≥2[/tex][tex]y≤-3x+2[/tex]
We can get the inequalities in the slope-intercept form, where m is the slope, and b is the y-intercept.
[tex]y=mx+b[/tex]
The second inequality is already in this form, it has a negative slope (–3), the y-intercept is at (0, 2), and the sign ≤ means the equation of the line is included, meaning the line in the graph will be continuous (if it wasn't the sign would be <). Additionally, it will be the y values less than or equal than the line.
On the other hand, the first inequality rearranged in the slope-intercept form is:
[tex]y≥x+2[/tex]
In this case, we have a positive slope, the y-intercept is also at (0, 2) and the sign is also included, but in this inequality, it means the y values are greater or equal than the line.
