Guide 3 Chapter 9 page 194 and 195

[kpkanupriyakhmi]

Q17:-
Qty A: The slope of line m
Qty B:-The slope of line n

Q18
Qty A:-Slope of line m
Qty B:--1

[n00bpron00bpron00b]

Q17)

Quantity A : Slope of line m
Quantity B : Slope of line n

Few important points regarding slopes before we dive into the solving part -

1) Line passing through quadrant 2 & 4 will always have a negative slope. Similarly line passing through quadrant 1 & 3 will always have a positive slope.

2) Another estimation method is to actually trace the given line from "left to right" ; while tracing from left to right if the line inclines downwards the slope is negative ; if the line inclines upwards (again from left to right) the slope is positive

(IMP) 3) The magnitude/Absolute value of slope increases as the line becomes more steeper

Now the solving part,

We know both the lines have negative slopes.

If you observe the diagram, you'll notice that line "n" is more steep (in inclination) compared to line "m"

Also keep in mind we are comparing the magnitude (just the physical values without any sign or direction)

Since line "n" is more steeper it will have a greater magnitude ; let's assume 3 (magnitude of line n = 3)

line "m" is less steeper as compared to line "n" ; so the magnitude will be less than line "n". Let's assume magnitude of line m = 2

Now, since the slopes are negative just add the negative sign in front of both magnitudes

Magnitude of line n = 3 -> negative slope = -3
Magnitude of line m = 2 -> negative slope = -2

Now compare both the slopes

line n slope = -3
line m slope = - 2

So Quantity (A) is greater (-2 > -3)

Just be careful while assuming slopes in the negative quadrant ; and don't get confused between magnitude and actual slope values.

In positive quadrant
-> steeper line will have greater magnitude and greater slope

In negative quadrant
-> steeper line will have greater magnitude but lesser slope (because of the negative sign)


Q18)

Given :

Co-ordinates of point Q (-3,2)
Line "m" passing from through quadrant (2), (4) and origin

Quantity A: slope of line m
Quantity B: -1

Slope formula = (y2-y1)/(x2-x1)

(x1,x2) & (y1,y2) co-ordinates for line m -

Notice the diagram, the line passes above point Q (i.e. -3,2)

(x1,x2) = (-1,1)
(y1,y2) = (0,0) - line passes through the origin

(0-0)/(1-(-1))
0/2 = 0

Quantity (A) greater

(x1,x2) = (-2,2)
(y1,y2) = (2,-2)

(-2-2)/(2+2) = -4/4 = -1

Both equal (C)


Hence (D)

[tommywallach]

Great explanations from noob. Just to be clear, he's being incredibly thorough, but the gist is quite simple.

17: N has a steeper downward slope. Anything downward is negative, and the steeper it is, the bigger the numerator and the smaller the denominator (rise over run). If we're comparing:

-big numerator/small denom WITH -small numerator/big denom

The latter will be closer to zero, and thus bigger, so the shallower line has the larger slope.

18. The only way we could know if this thing was more or less than -1 is if we had point Q at a point along the line for slope = -1 (i.e. -2, -2). As it is, we don't know this line's actual relationship to that line, which forces (D).

-t

[kpkanupriyakhmi]

@noob
could not understand (x1,x2) = (-1,1)
(y1,y2) = (0,0) - line passes through the origin

(0-0)/(1-(-1))
0/2 = 0

and

@ Tommy can you please elaborate more on the explanation?

[n00bpron00bpron00b]

@noob
could not understand (x1,x2) = (-1,1)
(y1,y2) = (0,0) - line passes through the origin

(0-0)/(1-(-1))
0/2 = 0

I just picked two points that lie on the line to calculate the slope.

1st point that lies on the line (x1,x2) = (-1,1)
x1 is the x - co-ordinate and x2 is the y - co-ordinate of the point.

2nd point that lies on the line (y1,y2) = (0,0)
since the line passes through the origin.

y1 is the x- co-ordinate and y2 is the y - co-ordinate of the point.

Now using these two sets of points (which lie on the line), calculated the slope.

slope (m) = (y2-y1)/(x2-x1)

[tommywallach]

Hey KP,

Honestly, I'd rather not elaborate, because saying more will only muddy the issue. If there's some aspect of my explanation that doesn't make sense, please feel free to point it out to me, along with your question about it. I'd encourage you to DRAW the line through the origin for slope = -1 and compare it to the line that is written. I think if you're staring at those, my explanation should make sense.

-t