+0  
 
0
283
6
avatar

whats the rule for my table?

-4  6

 4  4

 8  3

12 2

and what is an equation for the rule?

Guest Dec 3, 2014

Best Answer 

 #6
avatar+19197 
+5

whats the rule for my table?

-4  6

 4  4

 8  3

12 2

and what is an equation for the rule?

$$\small\text{
\begin{array}{c|c|c}
\hline
n & a_n & \small{\text{difference (d)}} \\
\hline
1 & 16 & \\
& & -4\\
2 & 12 \\
& & -4\\
3 & 8 \\
& & -4\\
4 & 4 \\
& & -4\\
5 & 0 \\
& & -4\\
6 & -4 \\
\hline
\end{array}
}}$$

$$\boxed{ a_n = a_1 + (n-1)*d } \small{\text{ arithmetic series }}$$

$$a_1 = 16 \small{\text{ and }} d = -4\qquad a_n = 16 + (n-1)*(-4) \\
a_n = 16 - 4n + 4\\
a_n = 20 - 4n \\
\small{\text{The equation for }} a_n \small{\text{ is }}
\textcolor[rgb]{1,0,0}{a_n = 20 - 4n } \\ \\
n? \qquad a_n = 20 - 4n \\
4n = 20 - a_n \quad | \quad : 4 \\
n = 5 - \frac{1}{4}a_n \\
\small{\text{The equation for }} n \small{\text{ is }}\textcolor[rgb]{1,0,0}{5 - \frac{1}{4}a_n }$$

heureka  Dec 3, 2014
Sort: 

6+0 Answers

 #1
avatar+17721 
+5

The formula for slope is:  m  =  (y2 - y1) / (x2 - x1)

The slope from (-4, 6) to (4, 4) is:  m  =  (4 - 6) / (4 - -4)  =  -2/8  =  -1/4

The slope from (4, 4) to (8, 3) is:  m  =  (3 - 4) / (8 - 4)  =  -1/4 

The slope from (8, 3) to (12, 2) is:  m  =  (2 - 3) / (12 - 8)  =  -1/4

Since the slope is always the same, these points fall on a straight line.

The point-slope formula for a straight line is:  y - y1  =  m(x - x1)

Using (x1, y1) = (-4, 6) and m = -1/4:          y - 6  =  (-1/4)(x - -4)

                                                                       y - 6  =  (-1/4)(x + 4)

                                                                        y - 6  =  (-1/4)x - 1

                                                                        y  =  (-1/4)x + 5

Melody, you are correct, so I'll modify my answer.

geno3141  Dec 3, 2014
 #2
avatar+92162 
+5

I think it is just

y= -1/4x+5

Melody  Dec 3, 2014
 #3
avatar+1090 
+5

If geno3141 is correct, wouldn't it simplify further to y  =  (-1/4)x + 11?

Mathematician  Dec 3, 2014
 #4
avatar
+5

thank you guys sooo much got er' down! thanks again!

Guest Dec 3, 2014
 #5
avatar+1090 
+5

First let me test the rule:

$${\mathtt{\,-\,}}{\mathtt{0.25}}{\mathtt{\,\times\,}}\left(-{\mathtt{4}}\right){\mathtt{\,\small\textbf+\,}}{\mathtt{5}} = {\mathtt{6}}$$

$${\mathtt{\,-\,}}{\mathtt{0.25}}{\mathtt{\,\times\,}}\left({\mathtt{4}}\right){\mathtt{\,\small\textbf+\,}}{\mathtt{5}} = {\mathtt{4}}$$

$${\mathtt{\,-\,}}{\mathtt{0.25}}{\mathtt{\,\times\,}}\left({\mathtt{8}}\right){\mathtt{\,\small\textbf+\,}}{\mathtt{5}} = {\mathtt{3}}$$

$${\mathtt{\,-\,}}{\mathtt{0.25}}{\mathtt{\,\times\,}}\left(-{\mathtt{4}}\right){\mathtt{\,\small\textbf+\,}}{\mathtt{5}} = {\mathtt{6}}$$

It looks like Melody is accurate.

Mathematician  Dec 3, 2014
 #6
avatar+19197 
+5
Best Answer

whats the rule for my table?

-4  6

 4  4

 8  3

12 2

and what is an equation for the rule?

$$\small\text{
\begin{array}{c|c|c}
\hline
n & a_n & \small{\text{difference (d)}} \\
\hline
1 & 16 & \\
& & -4\\
2 & 12 \\
& & -4\\
3 & 8 \\
& & -4\\
4 & 4 \\
& & -4\\
5 & 0 \\
& & -4\\
6 & -4 \\
\hline
\end{array}
}}$$

$$\boxed{ a_n = a_1 + (n-1)*d } \small{\text{ arithmetic series }}$$

$$a_1 = 16 \small{\text{ and }} d = -4\qquad a_n = 16 + (n-1)*(-4) \\
a_n = 16 - 4n + 4\\
a_n = 20 - 4n \\
\small{\text{The equation for }} a_n \small{\text{ is }}
\textcolor[rgb]{1,0,0}{a_n = 20 - 4n } \\ \\
n? \qquad a_n = 20 - 4n \\
4n = 20 - a_n \quad | \quad : 4 \\
n = 5 - \frac{1}{4}a_n \\
\small{\text{The equation for }} n \small{\text{ is }}\textcolor[rgb]{1,0,0}{5 - \frac{1}{4}a_n }$$

heureka  Dec 3, 2014

34 Online Users

avatar
We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details