https://sat.collegeboard.org/practice/sat-skills-insight/math/band/500/skill/8
Mathematics, 500-590, Skill Group 8, Question 1, why is the answer A.
Please explain I would think it would be just r/s since the two negative signs should cancel eachother out.
There are not two negative signs. On the y-axis, you go further down (negative) as you proceed to the right. On the x-axis, you go more right (positive).
This is what I have so far, dy/dx = m. Therefore - ( r-0)/(0-s). The - sign outside is due to the gradient sloping downwards. This simplifies too: - (r/-s) = (r/s).
I am not sure where I have gone wrong, and I don’t understand what you mean by further down, how do you know which value is larger.
Regards
There should be no negative outside “due to it sloping downwards.” That’s what you’re trying to figure out with the subtracting.
The value of y decreases as you follow the graph left to right. See? You start at the y-axis, where y = r. Then as you move right, y = 0. And then y goes negative. Your “rise” (from “rise over run”) is negative. It would actually be 0 - r.
Your x-value, on the other hand, gets more positive from left to right. Imagine numbers on this graph. If y goes from 3 to 0, x goes from (for example) 0 to 2. The change in x (2 - 0) is positive. The change in y (0 - 3) is negative. Slope is change in y over change in x. -r/s.
Look up what a positive slope looks like. Positive r/s would look completely different.
Thanks for the reply, so essentially if modelling it as a triangle which it is, the answer is the -(hypotenuse) which would be -r/s.
I kind of get your answer and thank you for helping me, but can you tell me why it is not:
dy/dx = -(0-r/s-0) = r/s. I understand that the answer has to have a negative sign due to the slope, but for other SAT questions similar to this I generally do the difference of y and x values between the 2 points.
Regards.
That equation you just put there is -dy/dx.
dy/dx is literally just the change in values. No extra negatives, no input from which way the graph is sloping. If you put an extra negative, that is now -dy/dx and is no longer representative of the slope.
I now understand it, thank you for taking the time to help me out. I really appreciate it, best of luck in your studies!