If f is a linear function of f(6)=7 and f(8)=12, what is the slope of the f in the xy-plane?
2006-06-17 05:05:31 · 12 answers · asked by redalert 2 in Science & Mathematics ➔ Mathematics
This is basic
slope= m=(y2-y1)/(x2-x1)=(12-7)/(8-6)=5/2
angle=arctan(5/2)
2006-06-17 05:53:32 · answer #1 · answered by Edward 7 · 0⤊ 0⤋
You know how to get remainders when you do division, right? It might have been a long time, since you've probably been working with decimals and fractions for a while. So just a quick review - if you divide 13 by 3, then how many times does 3 go into 13 evenly? Four, right? So 4x3 = 12, and 13 - 12 gives you the remainder of 1. If you did the long division, it would look like .__4 r 1 3)13 . -12 ------- ... 1 Okay. One way to get the answer is to find an n that satisfies all the conditions you're given in the problem. This is actually pretty easy, since there's only one condition - n/9 gives a remainder of 7. So, if you take n = 7, then n/9 = 0 r 7. Okay, now, 5n = 5*7 = 35, and 35/9 = 3 r 8. So, the remainder is 8. If you want a more rigorous answer, you could do it like this: positive integer n divided by 9 is equal to a positive integer x with a remainder of 7. So, n / 9 = x r 7 n = 9 * (x r 7) n = 9x + 7 5n = 5*(9x + 7) 5n = 45x + 35 5n / 9 = (45x + 35) / 9 5n / 9 = 45x / 9 + 35 / 9 5n / 9 = 5x + 35 / 9 5n / 9 = 5x + (27 + 8) / 9 5n / 9 = 5x + 27/9 + 8/9 5n / 9 = 5x + 3 + 8/9 Then, since x is an integer, 5x + 3 is an integer. So, in remainder form, 5n / 9 = (5x + 3) r 8. So you wind up with the same answer. Hope this helps!
2016-05-19 22:46:57 · answer #2 · answered by Anonymous · 0⤊ 0⤋
As the function, f, is linear, let f(x) = mx + c
6m + c = 7 ---(1)
8m + c = 12 --(2)
(2) - (1),
2m = 5
m = 5/2 = 2.5
So the slope of f is 2.5.
2006-06-17 09:51:42 · answer #3 · answered by Kemmy 6 · 0⤊ 0⤋
5/2
2006-06-17 05:15:09 · answer #4 · answered by Anonymous · 0⤊ 0⤋
The two points you have are (6,7) and (8,12).
The slope is therefore:
(12-7)/(8-6) = 5/2.
2006-06-17 05:49:30 · answer #5 · answered by loki_knows 4 · 0⤊ 0⤋
this is the same thing as telling you two points
(6,7) and (8,12)
m = change in y's/ change in x/s
m = (12-7)/ (8-6) = 5/2
2006-06-17 06:12:46 · answer #6 · answered by Mary B 1 · 0⤊ 0⤋
the f(x) is the y and what it equals is the x. Then you use the slope change formula(change in y / change in x). so it would be 2/5.
2006-06-17 05:13:52 · answer #7 · answered by sportsmess 3 · 0⤊ 0⤋
slope = m
m= (y-y)/(x-x)
points = (6,7) (8,12)
(12-7)/(8-6) = 5/2
2006-06-17 06:18:04 · answer #8 · answered by limelight_story 2 · 0⤊ 0⤋
I never took the SAT. It's obvious to me now, that it wouldn't have done any good. That problem is completely foreign to me. I know I'm not much help, but wanted to tell you good luck.
2006-06-17 05:10:49 · answer #9 · answered by Anonymous · 0⤊ 0⤋
delta Y / delta X = 5/2
2006-06-17 08:01:07 · answer #10 · answered by Jeremy W 2 · 0⤊ 0⤋