Respuesta :
Answer:
both of the points satisfy the given inequality, confirming they are solutions.
Step-by-step explanation:
The points (-3,7) and (9,-5) lie on the boundary line, and the points (-4,2) and (6,-5) are solutions of the inequality; to further investigate, we can examine the situation in the following manner:
1. Calculate the slope of the boundary line using the points (-3,7) and (9,-5):
Slope = (y2 - y1) / (x2 - x1)
Slope = (-5 - 7) / (9 - (-3))
Slope = (-12) / (12)
Slope = -1
2. Write the equation of the boundary line using the point-slope form with the slope calculated in step 1 and one of the given points, for example, (-3,7):
y - y1 = m(x - x1)
y - 7 = -1(x - (-3))
y - 7 = -x - 3
y = -x + 4
3. Check if the points (-4,2) and (6,-5) satisfy the inequality represented by the boundary line equation y < -x + 4:
For (-4,2): 2 < -(-4) + 4 => 2 < 0 + 4 => 2 < 4 (True)
For (6,-5): -5 < -(6) + 4 => -5 < -2 + 4 => -5 < 2 (True)
So, both of the points (-4,2) and (6,-5) satisfy the given inequality, confirming they are solutions.
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- Brainly
https://brainly.com/question/48077965
