Which statements are true about the linear inequality y > x – 2? Check all that apply.
The slope of the line is –2.
The graph of y > x – 2 is a dashed line.
The area below the line is shaded.
One solution to the inequality is (0, 0).
The graph intercepts the y-axis at (0, –2).
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Answer:
Statements No. 2, 3, 4, 5 are true
Step-by-step explanation:
Given linear inequality is
y > x - 2
The equation can be written in equation form as
y = x - 2 .... (A
Comparing equation (A) with standard equation of line y = mx +c, we find that
m= 1
c = -2
Now m represents the slope of line and c represents the point where line touches y axis.
Now lets check correct statements.
- The slope of line is 1, so our first statement is wrong.
- The graph of line will be dashed as the the inequality has only greater than sign, so our statement is correct.
- if we substitute x= 0 and y =0 in the above equation we get 0 > -1. This statement is true so the solution of the inequality will lie below the line and toward the origin. The solution region is always shaded, so our statement is correct.
- As we have checked in the above point (0, 0) satisfy the above equation, so our statement is correct.
- As we know the graph touches the y axis at c = - 2, so our statement is correct.
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