A line has slope -5/3. Through which two points could this line pass?
A: (12,13), (17,10)
B: (16,15), (13,10)***
C: (0,7), (3,10)
D: (11,13), (8,18)***
My Explanation: I know how to use the formula for slope, which is y2 -y1 over x2 - y2, so I know how to solve the problem. The thing I'm struggling with is that when I solved the problem using the forumla for the answers 2 and 4, it got the same answer. Lets dial it down. Using the formula for answer 2, it leads to 10 - 15 which is -5 and 13 - 16 which is -3, so its -5/-3. Couldn't -5/-3 also be -5/3? Because -5/3 is the solution when using the forumla for answer 4. Thank you if you read all of this. I appreciate the feedback and support!
Hi! Rate of Change and Slope Answers:
1. C -1/3
2. D (11,13),(8,18)
3. B -2
4. D Undefined
5. D 55/1
Hope this helps!
After thinking about it, two negatives cancel out to be neutral so the answer is D. No need for any feedback now.
Thanks, Hinata, if you go to Connexus those answers are correct. Just got a 100%.
can we get all the answers LMAO
m = (y2 - y1) / (x2 - x1)
if x and y change in the SAME direction (up or down), then the slope is positive
if they change in opposite directions, the slope is negative
-5/-3 is not the same as -5/3
... one is positive, the other negative
You are correct in noticing that when you calculate the slope for both options 2 and 4, you obtain the same value of -5/3. However, we need to be careful in making our final decision because the slope is just one piece of information when determining if a line passes through two particular points.
To confirm which option is correct, we can plug the coordinates of each point into the equation of the line and see if it holds true for both points.
Taking option B as an example:
We have the points (16,15) and (13,10). Let's calculate the slope using the formula you mentioned:
slope = (y2 - y1) / (x2 - x1) = (10 - 15) / (13 - 16) = -5 / -3 = 5/3 not -5/3.
Since the calculated slope (-5/3) does not match the given slope of the line (-5/3) for option B, this means that option B is not correct.
You can repeat this process with the other options to find the correct choice.