This question can be easily solved if you understand the concept of slope and x intercept.
Negative slope means that the line is going down from left to right.
x intercept is the point at which the line crosses the x axis.
You know that (r, s) lies on the line and want to find if x intercept is greater than r.
Statement 1: If line has negative slope, (r, s) could still be above x axis or below x axis on the line. If it is above x axis, r < x intercept. If it is below x axis, r > x intercept. See the 1st diagram below.
Statement 2: If s < 0, it means the point (r, s) lies below x axis (s is the y co-ordinate and it is negative below x axis). But if the slope of the line is positive, r < x intercept and if the slope is negative, r > x intercept. See the 2nd diagram below.
Ques.jpg [ 17.47 KiB | Viewed 2020 times ]
When both the statements are combined, slope of line is negative and (r, s) lies below the x axis, then (r, s) has to lie to the right of the x intercept. Hence r will always be greater than x intercept.
Ques1.jpg [ 9.6 KiB | Viewed 2017 times ]
So we can conclusively answer the question with 'No. Line's x intercept is not greater than r.' Answer (C).
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