Assess whether the three points (0,4), (7, -6) and (-7,14) lie on a line.
I'm doing y2-y1/x2-x1.
If I do 0,4 and 7,-6 in the above we get 10/7
If I do 0,4 and -7,14, I get -10/-7
I assume these two are the same if the above is correct?
Yes, they both reduce to 10/7 : )
yes, but you made an error twice in calculation the slope
using (0,4) and (7,-6) , the slope
= (-6-4)/(7-0) = -10/7
using (0,4) and (-7,14) , the slope
= (14-4)/(-7-0) = 10/-7
recall that a negative divided by a positive is negative, so
-10/7 = 10/-7
so since the slopes of your two segments are the same, and you used
(0,4) as a "link" for the two segments, they all lie on the same line
Awesome thanks! Sorry, might have questions for a bit ;) I take a online class over here but they give no proper hints bar like 5-7 10 minute youtube videos (And yes this is an actual adult highschool I take!) and half of it doesn't feel like the stuff on the homework. It's a bit frustrating!
Ah right, my bad! Thanks!
To determine if the three points (0,4), (7,-6), and (-7,14) lie on a line, we can use the slope formula and check if the slopes between any two points are equal.
Let's calculate the slope between the first two points: (0,4) and (7,-6).
Using the formula: slope = (y2 - y1) / (x2 - x1), we have:
slope = (-6 - 4) / (7 - 0) = -10 / 7.
Now, let's calculate the slope between the first and third points: (0,4) and (-7,14).
Using the same formula: slope = (y2 - y1) / (x2 - x1), we have:
slope = (14 - 4) / (-7 - 0) = 10 / -7 = -10 / 7.
As you correctly computed, the slopes between the first and second points and the first and third points are equal, both being -10/7.
If the slopes between any two points are equal, it indicates that the three points lie on the same line. Therefore, based on the slopes, we can conclude that the points (0,4), (7,-6), and (-7,14) lie on a line.