Help me Plzz I need help with this !!
2 answers:
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Answer:
D
Step-by-step explanation:
To find the system of inequalities, we simply need to find the equation of each line.
So, let’s find the inequality that is represented by each line.
Red Line:
First, let’s determine the slope. To do so, we can use the slope formula:
We can use any two points. Let’s use (0, 1) and (1, 3). Substituting them into the slope formula yields:
Therefore, the slope of the red line is 2.
Now, let’s figure out the rest of the equation. We can use the slope-intercept form:
Notice that our y-intercept of our red line is (0, 1). Therefore, substitute 1 for b and 2 for m. This yields:
Now, we need to determine our sign. Notice that the shaded region is below the red line. Therefore, y is less than our equation.
And since our line is shaded, our sign will be less than or equal to. Therefore:
Blue Line:
Again, let’s first find the slope. We can use the two points (0, 2) and (2, 3). Thus:
So, the slope is 1/2.
We can now use the slope-intercept form. Notice that our y-intercept is (0, 2). So, substitute 1/2 for m and 2 for b. This yields:
Finally, we will determine our sign. Since the shaded region is above the blue line, our y is greater than our equation. And since it’s shaded, our sign is greater than or equal to. Therefore, our equation is:
Thus, all together, our inequalities are:
Therefore, our answer is D