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 [tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
Then the slope of the line [tex]m=\frac{1-0}{0-(-1)}=1[/tex]
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 [tex]m=\frac{0-(-2)}{2-0}=1[/tex]
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
Learn more:
You can learn more about the solution of the inequality in brainly.com/question/7490805
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