Question

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

y > x – 2 and y < x + 1
y < x – 2 and y > x + 1
y < x – 2 and y > x + 1
y > x – 2 and y < x + 1

Answer 1

The system of linear inequalities which represented by the graph is:

y > x - 2 and y < x + 1

Step-by-step explanation:

The first line has positive slope and passes through points (-1 , 0) and

(0 , 1)

The slope of the line is $m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

Then the slope of the line $m=\frac{1-0}{0-(-1)}=1$

The line intersects y-axis at point (0 , 1), then the y-intercept is 1

The form of the equation of a line is y = mx + c, where m is the slope

of the line and c is the y-intercept

∵ m = 1 and c = 1

∴ The equation of the line is y = x + 1

Now we need to write the inequality which represented by the 1st

line in the graph, using the important points

1. The line is a dashed straight line, so the sign of inequality is > or <

   without equal

2. Everything to the right of the line is shaded, means the shaded is

    under the line, so the sign of inequality is <

∴ The inequality is y < x + 1

The second line has positive slope and passes through points (0 , -2)

and (2 , 0)

Then the slope of the line $m=\frac{0-(-2)}{2-0}=1$

The line intersects y-axis at point (0 , -2), then the y-intercept is -2

∵ m = 1 and c = -2

∴ The equation of the line is y = x - 2

Now we need to write the inequality which represented by the 2nd

line in the graph, using the important points

3. The line is a dashed straight line, so the sign of inequality is > or <

   without equal

4. Everything to the left of the line is shaded, means the shaded is

    over the line, so the sign of inequality is >

∴ The inequality is y > x - 2

The system of the linear inequalities represented by the graph is:

y > x – 2 and y < x + 1

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Answer 2

Answer:

Its D

Step-by-step explanation:

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