The graph of the line y = mx + b is shown. Which of the following is

Question

https://gmatclub.com/forum/download/file.php?id=47024 The graph of the line y = mx + b is shown. Which of the following is true? (A) mb < -1 (B) -1 < mb < 0 (C) mb = 0 (D) 0 < mb < 1 (E) mb > 1 2004_AMC_12A_Problem_5.png

Archit3110 · Answer

slope of the line = -1/2
so seeing options 
IMO B is correct

kukretipiyush · Answer

Can anyone explain answer to this question??

prashanths · Answer

In the equation given, b is the y-intercept, i.e., when x is 0 (where the line meets the y-axis). So, from the graph, 0 < b < 1.

m (slope) = (y2-y1)/(x2-x1)
Consider two points where the line meets the axes.
The line meets y-axis at (0,0.8) approx and x-axis at (1.8,0) approx.

m = (0.8-0)/(0-1.8) = - ve value between 0 and -1

So, m x b would be between 0 and -1.

aliakberza · Answer

Looking at the graph we can see that the Y intercept is slightly below 1 and the x intercept is slightly below 2. If the y and x intercepts were exactly 1 and 2 the slope (or m) of the line would have been -1/2. So we know that the slope is slightly less than -1/2. Also note that b is the y-intercept and is <1 . The product of mb will be a negative fraction as ~1 * ~ -1/2 ~= -1/2. Now lets consider the options: (A) mb < -1: Not possible as m is -1/2 and b is ~=1 so mb is a negative fraction so has to be >-1. Option A would have been possible only when b>=2 (B) -1 < mb < 0 : Yes, as given above because m~= -1/2 and b~=1, mb has to be a negative fraction (C) mb = 0 : A product of two numbers will be zero only when one of the two numbers is zero and that is clearly not the case (D) 0 < mb < 1 : Not Possible as b>0 and m<0 so mb<0 (E) mb > 1 : Not possible as b>0 and m<0 so mb<0 So answer is B

CrackverbalGMAT · Answer

Since the line is going down from left to right, it has a negative slope. So m is negative. But, the line is intersecting the y-axis above the origin; so the y-intercept is positive, which means ‘mb’ should be negative.

We can eliminate options C, D and E on the basis of the above reasoning.

Let’s assume the x-intercept of this line to be (2,0) and the y-intercept to be (0,1).
 
The slope intercept form of the equation of a straight line is given by y = mx + c, where m is the slope of the line and c is the y-intercept.

In our case, the line y = mx + b means a line having a slope m and y-intercept b. Since we have taken the y-intercept as 1, we can say b = 1.

Also, since the line is passing through (2,0) and (0,1) we can calculate its slope as -1/2. This means m = - \frac{1}{2} .

Therefore, mb = - \frac{1}{2} . This is clearly a negative proper fraction. So, the correct answer option is B.

Note that we have assumed (2,0) and (0,1) as the intercepts, but, as per the question, the x and the y intercepts should be less than 2 and 1 respectively. This does not change the fact that mb will be a negative proper fraction, though.

Hope this helps!

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The graph of the line y = mx + b is shown. Which of the following is

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The graph of the line y = mx + b is shown. Which of the following is

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