Question

Is this relationship a function ?

Rewarding Medal to first best answer.
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Answer 1

If there is a single domain value for every range value then it's a function. So yes this is a function.

Answer 2

so how can i explain this function in an equation for instance ?

Answer 3

@sarara

Answer 4

@whpalmer4

Answer 5

well, what happens if you plot these points on a piece of graph paper. what do you get?

Answer 6

i think a straight line going downwards

Answer 7

correct ? @whpalmer4 and does this point toward the part c) which is graphing this table ?

Answer 8

yes, a straight line with negative slope. Could you figure out the slope from a pair of points?

Answer 9

yes

Answer 10

y=mx+b
right

Answer 11

@whpalmer4

Answer 12

sorry, had to give my cat a shot!

Answer 13

oh ahaa np lol

Answer 14

well, that's a formula for a line, yes, but we need to find the value of \(m\)

Answer 15

so we can represent the relationship in an equation right ?

Answer 16

yes. the formula to find the slope of the line connecting two points \((x_1,y_1)\) and \((x_2,y_2)\) is \[m = \frac{y_2-y_1}{x_2-x_1}\]does that look familiar?

Answer 17

yes

Answer 18

it does @whpalmer4

Answer 19

Good. Pick two points out of your data table, and find the slope of the line with that formula, please.

Answer 20

ok for instance the first and last one @whpalmer4

Answer 21

any two points will do.

Answer 22

ok ill pick the first and last ones

Answer 23

i got -2 @whpalmer4

Answer 24

as the slope

Answer 25

no, that is not correct. can you show me your work?

Answer 26

i plugged in y2 and y1 and x1 and x2 subtracted both from each other and the divided

Answer 27

x1=0
x2=3

Answer 28

y1=4
y2=1

Answer 29

0-4=-4
3-1=2

Answer 30

-4/2=-2

Answer 31

@whpalmer4

Answer 32

oh and i actually have to go now so i wont be here to finish the rest of my work but ill be back on tomorrow and i'll re-post this question @whpalmer4

Answer 33

Don't repost, we'll finish it here.

Answer 34

ok thanks bye for now

Answer 35

Here's your table, for easy reference:
\[\begin{array}{cc}
x & y\\\hline\\0 & 4 \\
1 & 3 \\
2 & 2 \\
3 & 1 \\
\end{array}\]

Answer 36

using the first and last points as you did:

\((x_1,y_1) = (0,4)\)
\((x_2,y_2) = (3,1)\)
Slope of line connecting the two:
\[m = \frac{y_2-y_1}{x_2-x_1} = \frac{1-4}{3-0} = \frac{-3}{3} = -1\]

Answer 37

so our line will have slope \(m = -1\) and will be \(y = -1x + b\) where \(b\) is a value yet to be determined. However, we can find it by plugging in any point from the table and solving for \(b\), such as \((0,4)\)
\[4 = -1(0)+b\]\[b=\]

Now you have an equation for the points in the table. You should try it out with the other points and make sure you agree that it fits them all.