Line D passes through point (-2,5), and the product of its x-intercept and y-intercept is positive. Which of the following points could be on line D?

A. (5,10)
B. (-3,2)
C. (-1,7)
D. (-1,2)
E. (-3,1)

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Anyone can clarify the meaning of "the product of its x-intercept and y-intercept is positive" on the diagram for me?

Thanks

I think this means we are looking for a line that has negative slope.

Only D satisfies that condition.

Point (-2,5)

A. (5,10) m = 10 - 5/ 5 -(-2) = +ve
B. (-3,2) m = 2-5 / -3 - (-2) = +ve
C. (-1,7) m = 7 - 5 / -1 - (-2) = +ve
D. (-1,2) m = 2 - 5 / -1 - (-2) = -ve
E. (-3,1) m = 1 - 5 / -3 - (-2) = +ve

First and foremost, make sure you draw quick diagrams in coordinate geometry problems. Half your problem will be solved there and then.
So the line would look something like one of these lines if it passes through (-2, 5).



Further, x-intercept is the point on the x axis where the line intersects the x axis. y intercept is the point on the y axis where the line intersects the y axis. Say if a line passes through (1, 0), its x intercept much be 1. If a line passes through (0, -3), its y intercept must be -3. Of course, for any straight line, x and y intercepts have unique values.

What is the point of giving that the product of x and y intercepts is positive? This implies that either both x and y intercept are positive or both are negative. Now look at the lines above. Would it look something like the green line or the red line?
The red line has negative x intercept and positive y intercept so the product of its intercepts will be -ve. Hence, it cannot be the required line.
The green line has both intercepts positive so it can be our line ( it is downward sloping from left to right hence it has negative slope)
Now, I have plotted the approximate position of all the points. Which one can possibly lie on this line?

I think it is quite clear that the line can only pass through (-1, 2) and still maintain the negative slope. In all other cases, the line would have a positive slope i.e. it will look like the red line
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Here is how i approached the question:
Equation of a line is (y-y1)/(x-x1)=m
y1= 5 , x1 = -2

(y-5)/(x+2)=m
y-5=mx+2m
y=m(x+2)+5

If both the x-intercept and y-intercept are positive, if you draw the line then the slope of the line would be -ve.

Plug in the solutions y=m(x+2)+5, only D will give you a -ve value for m, thus it's the solution , thanks !

Thanks for the excellent explanation; Can you please update new question checking similar concept?

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