Answer: Choice C
y is greater than or equal to -3
y is less than or equal to (5/3)x + 2
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Explanation:
The horizontal blue line is the graph of y = -3. Every point on this line has a y coordinate of -3 while x can be anything you want. Example points include (1,-3) and (5,-3). Shading above this boundary line leads to the graph of [tex]y \ge -3[/tex] (y is greater than or equal to -3). The answer is between choice B or choice C based on this so far.
The other boundary line is y = (5/3)x + 2. This can be found using the slope formula through the two points (0,2) and (-3,-3) which are both on the diagonal blue line. You should find the slope to be m = 5/3. Then you'll use the point slope form with the slope you found, plus some other point, to find the equation above.
Note how the shading is below the diagonal line. So we'll shade below the line y = (5/3)x + 2 meaning we have this second inequality [tex]y \le \frac{5}{3}x+2[/tex] (y is less than or equal to 5/3 times x +2)
So overall, those two inequalities point to choice C as the final answer
The inequality which describes this graph is:
[tex]y\geq -3[/tex]
[tex]y\leq \dfrac{5}{3}x+2[/tex]
By looking at the graph we observe that both the inequalities are inequalities with a equality sign i.e. not strict.
Since, both the line are solid.
Hence, the inequality which satisfies this condition is:
y≥−3.
Now the equation of a line passing through (0,2) and (-3,-3) is given by:
[tex]y-2=\dfrac{-3-2}{-3-0}\times (x-0)\\\\y-2=\dfrac{-5}{-3}\times x\\\\y-2=\dfrac{5}{3}x\\\\y=\dfrac{5}{3}x+2[/tex]
Hence, the inequality will be:
[tex]y\leq \dfrac{5}{3}x+2[/tex]
