Which statements are true about the graph of y s 3x + 1 and y 2 -x + 2? Check all that apply. O The slope of one boundary line is 2.
O Both boundary lines are solid.
A solution to the system is (1, 3).
O Both inequalities are shaded below the boundary lines
O The boundary lines intersect.

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Explanation:

Let's go through each of the answer choices to see which are true and which are false.

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Choice A

The general slope intercept form is y = mx+b

m = slope and b = y intercept.

For y = 3x+1, the boundary line of the first inequality, the slope is 3.

For y = -x+2, the slope is -1.

None of the slopes are 2.

Choice A is false.

We'll use the concept of slope again in choice E.

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Choice B

The "or equal to" part of the inequality sign is what directly determines the boundary line being solid. This is because we include points on the boundary.

Choice B is true.

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Choice C

Plug x = 1 and y = 3 into the first inequality

The last inequality is true, so the first inequality is true when (x,y) = (1,3). This makes (1,3) a solution to

Repeat those steps for the other inequality given to us

which is also true, so that makes (1,3) also a solution to

The point (1,3) is a solution to both inequalities at the same time, making it a solution to the system overall.

Choice C is true

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Choice D

When y is fully isolated, the "less than" inequality indicates the shading is below the boundary. This is due to us considering points of y coordinates smaller than the boundary line. So we'll shade below the boundary for

We don't do the same for . Instead, we'll shade above the solid boundary line.

Choice D is false.

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Choice E

If two lines have equal slopes, but different y intercepts, then we have parallel lines. Parallel lines never intersect.

If on the other hand, the slopes are different values, then the two lines will intersect somewhere on the xy grid. There will only be exactly one point of intersection.

The given system has boundary lines of slopes 3 and -1, for the first and second inequality respectively. Refer back to choice A.  These differing slopes tell us that the boundary lines intersect somewhere.

Choice E is true