You are right! Got it. I was too tired yesterday to get it right! Thanks!

I don't really get why the answer choices are B and C? I don't understand why thatyio make B true?

Could you please explain further?

That's a rule ; The slope of line n is always equal the negative reciprocal of perpendicular line m

My problem is in understanding the question! I understand completely why the solutions, but i don't understand the question.

It says which one guarantee that we will have a slope > 1 for line n.

Choice A: is sufficient because we have the case when a = b, and we might as well have slope larger than 1. So it should be true.

Choice B: insures that line n will have a slope of 1, so it should be false too.

Choice C: insure that we will have (c,c), which will always give slope of 1 for line n, so it should be false.

None of them guarantee that we will have slope larger than 1 except A.

@Avraheem, the question asks which of the options individually will help you determine if the slope of n will be greater than 1.

Options b and c give you concrete values - option B - slope is 1 - helps you determine if the line's slope is above 1, in this case it's not. Option C leads you towards a negative slope, which results in helping you decide if the slope is above 1 - nope.

Option A on the other hand, just tells you that the line doesn't pass through a point a,b where a>b and a and b are both positive. It could pass through any other points such that the slope will be positive or negative or 0. We can't use that particular information to decide whether the slope of line is above 1 or not. Hence B & C.

I think the choice c is missing a data it should say c and d are positive otherwise if you take c and d negative slope becomes 1 and if you take c and d positive slope is over 1

This question is purely ambiguous. It should say ' the slope is greater or equal to 1'.

C should not be right. "Line n passes through the point (c, d +1) where c and d are consecutive integers and c > d." It is not excluded that c = 0 and d = -1, so that the point (c, d+1) = (0, 0) which is the origin. In this case, statement c does not tell us anything more than what we were already given. Thus, c does not suffice to determine whether or not the slope is greater than 1.

probably phrase the question right

Carcass can you please explain how B and C? since all of the option can be of slop 1.

Statement I

Line n avoids points $\((\mathrm{a}, \mathrm{b})\)$ with $\(\mathrm{a}>0, \mathrm{~b}>0\)$, and $\(\mathrm{a}>\mathrm{b}\)$. This rules out first-quadrant points above the line $\(\mathrm{y}=\mathrm{x}\)$ (slope 1), but allows slopes $\(\leq 1\)$ or $\(>1\)$. For example, slope 0.5 passes through $\((2,1)\)$ where $\(\mathrm{a}=2>\mathrm{b}=1>0\)$, but slope 2 passes through no such points since $\(\mathrm{b}=(2 / 2) \mathrm{a}=\mathrm{a}\)$, so $\(\mathrm{a}=\mathrm{b}\)$, not $\(\mathrm{a}>\mathrm{b}\)$. Thus, insufficient.

Statement II

Line $\(\mathrm{m} \perp \mathrm{n}\)$ with slope -1 means slope of $\(\mathrm{n}=1\)$ (negative reciprocal of -1 ). Exactly 1 is not greater than 1 , so sufficient to determine no.

Statement III

Line n through $\((\mathrm{O}, \mathrm{O})\)$ and $\((\mathrm{c}, \mathrm{d}+1)\)$, with $\(\mathrm{c}, \mathrm{d}\)$ consecutive integers, $\(\mathrm{c}>\mathrm{d}\)$. Let $\(\mathrm{d}=\mathrm{k}\)$, then $\(\mathrm{c}=\mathrm{k}+1(\mathrm{k}\)$ integer). Point $\((k+1, k+1)\)$, slope $\(=(k+1) /(k+1)=1\)$, not $\(>1\)$. Sufficient to determine no.

Question, where does it say in Statement C that Line n passes through (0,0)? I've been having trouble on this one. Thanks for the explanation!

In the xy-plane, line n is a line that passes through the origin.

From the stem, the first line. This is valid to take into account for all the following three statements.

In fact the III is

Line n through $\((\mathrm{O}, \mathrm{O})\)$ and $\((\mathrm{c}, \mathrm{d}+1)\)$

I hope this helps