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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