Question

On a coordinate plane, 2 dashed lines are shown. The first straight line has a negative slope and goes through (0, 1) and (2, 0). Everything below and to the left of the line is shaded. The second straight line has a positive slope and goes through (negative 1, 0) and (0, 2). Everything above and to the left of the line is shaded. A point is shown at (negative 3, 1).
Which system of inequalities with a solution point is represented by the graph?

y > 2x – 2 and y < Negative one-halfx – 1; (3, 1)
y > 2x – 2 and y < Negative one-halfx + 1; (–3, 1)
y > 2x + 2 and y < Negative one-halfx – 1; (3, 1)
y > 2x + 2 and y < Negative one-halfx + 1; (–3, 1)

Answer 1

Answer:

Using the concepts of coordinate system and equation of line, we find that y ≥ (1/3)x + 3 and 3x-y > 2 are represented by the graph.

Step-by-step explanation:

Equation of line passes through points (a, b) and (c, d) is given by:

y-b = [(d-b) / (c-a)] / (x-a)

Given that the first solid line (≤ or ≥) has a positive slope and goes through (0, 3) and (3, 4).

y-3 = [(4-3) / (3-0)] / (x-0)

y-3 = x / 3

y - (1/3)x = 3

Also, everything above the line is shaded, i.e. the inequality represents the first graph: y ≥ (1/3)x + 3

The second dashed line (< or >) has a positive slope and goes through (0, - 2) and (1, 1).

y+2 = [(1+2) / (1-0)](x-0)

y+2 = 3x

3x-y = 2

Everything to the right of the line is shaded.

i.e. inequality represents the second graph: 3x-y > 2

Hence, the system of linear inequalities is represented by the graph :

y ≥ (1/3)x + 3

3x-y > 2

For more explanation, refer the following link:

https://brainly.com/question/13284474

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Answer 2

Answer:

D

Step-by-step explanation:

Got it right on edge 2022