Algebraic approach:Lines n and p lie in the xy-plane. Is the slope of line n less than the slope of line p?We have two lines:

y_n=m_1x+b_1 and

y_p=m_2x+b_2. Q: is

m_1<m_2?

(1) Lines n and p intersect at the point (5,1) -->

1=5m_1+b_1=5m_2+b_2 -->

5(m_1-m_2)=b_2-b_1. Not sufficient.

(2) The y-intercept of line

n is greater than the y-intercept of line

p --> y-intercept is value of

y for

x=0, so it's the value of

b -->

b_1>b_2 or

b_2-b_1<0. Not sufficient.

(1)+(2)

5(m_1-m_2)=b_2-b_1, as from (2)

b_2-b_1<0 (RHS), then LHS (left hand side) also is less than zero

5(m_1-m_2)<0 -->

m_1-m_2<0 -->

m_1<m_2. Sufficient.

Answer: C.

Graphic approach:Lines n and p lie in the xy plane. Is the slope of line n less than the slope of line p?(1) Lines n and p intersect at (5,1)

(2) The y-intercept of line n is greater than y-intercept of line p

The two statements individually are not sufficient.

(1)+(2) Note that

a higher absolute value of a slope indicates a steeper incline.

Now, if both lines have positive slopes then as the y-intercept of line n (blue) is greater than y-intercept of line p (red) then the line p is steeper hence its slope is greater than the slope of the line n:

Attachment:

1.PNG [ 14.29 KiB | Viewed 2030 times ]
If both lines have negative slopes then again as the y-intercept of line n (blue) is greater than y-intercept of line p (red) then the line n is steeper hence the

absolute value of its slope is greater than the

absolute value of the slope of the line p, so the slope of n is

more negative than the slope of p, which means that the slope of p is greater than the slope of n:

Attachment:

2.PNG [ 13.66 KiB | Viewed 2030 times ]
So in both cases the slope of p is greater than the slope of n. Sufficient.

Answer: C.

For more on this topic check Coordinate Geometry Chapter of Math Book:

math-coordinate-geometry-87652.htmlHope it helps.

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