bmahes wrote:
IanStewart wrote:
The conventional approach here would be to find the equation of the line. You can find the slope by subtracting the y coordinates of the two points, and then dividing by the difference in x coordinates:
m = (0 - 5)/(7 - 0) = -5/7
The y intercept of the line is 5, since (0,5) is on the line, so the equation of the line is
y = (-5/7)x + 5
If a point is on this line, then the equation above must be true if we plug in that point's coordinates. So we can now plug in each answer choice to see which works. If you plug in answer D (x = 14, y = -5), you get:
-5 = (-5/7)(14) + 5
-5 = -10 + 5
-5 = -5
so the equation is true, and D is on the line.
If you have a good conceptual understanding of slopes, you can bypass the calculations above. If a line travels from (0,5) to (7,0), it goes across 7 units and falls 5 units. So if we go across a further 7 units from the point (7,0), we must fall by a further 5 units. We'd then be at point (14,-5).
So I wanted to get this "good conceptual understanding of slopes" and not solve it by making equations. Can you please help me with it?
I have discussed the concept of slope here:
https://www.veritasprep.com/blog/2016/0 ... line-gmat/The points on the line are (0, 5) and (7, 0).
So for 7 units increase in x value, y decreases by 5 units. If x reduces by 7 units, y will increase by 5 units. So from (0, 5) we will get that (-7, 10) will lie on the line, not (-7, 5)
If x increases by 14 units, y will reduce by 10 units so from (0, 5), we will get (14, -5). This is option (D). Correct answer.
Some more examples:
If x reduces by 14 units, y will increase by 10 units so from (0, 5), we will get (-14, 15), not (-14, 10)
If x increases by 21 units, y will reduce by 15 units so from (0, 5), we will get (21, -10), not (21, -9)
I have read your blog (highly helpful) and have understood that if the slope here were +2 it would mean if x increases by 1 unit, y would increase by 2 units. In this question, the slope is -5/7 (a fraction) now how do we apply this logic here? How did you come to this conclusion "for 7 units increase in x value, y decreases by 5 units"