Mathematics, 22.08.2019 17:30 aidananderson

Ascatter plot is shown below: a graph shows numbers from 0 to 10 on the x axis at increments of 1 and the numbers 0 to 15 on the y axis at increments of 1. the ordered pairs 0, 15 and 1, 10 and 2, 12 and 3, 13 and 4, 7 and 5, 8 and 6, 8 and 7, 4 and 8, 5 and 9, 3 and 10, 0 are shown on the graph.
which two ordered pairs can be joined to best draw the line of best fit for this scatter plot?
a (0, 14) and (10, 14)
b (0, 14) and (10, 1)
c (0, 7) and (7, 0)
d (0, 7) and (3, 0)

Answers: 1

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Answers

Answer from: breniljakenotro

B (0, 14) and (10, 1)

Step-by-step explanation:

Option A: (0, 14) and (10, 14)

Equation of line using two point slope form .

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

(x_1,y_1)=(0,14)

(x_2,y_2)=(10,14)

Substitute values in formula :

$y-14=\frac{14-14}{`10-0}(x-0)$

y-14=0(x-0)

y=14

Option B : (0, 14) and (10, 1)

Equation of line using two point slope form .

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

(x_1,y_1)=(0,14)

(x_2,y_2)=(10,1)

Substitute values in formula :

$y-14=\frac{1-14}{`10-0}(x-0)$

$y-14=\frac{-13}{10}(x-0)$

$y=\frac{-13}{10}x+14$

Option C: (0, 7) and (7, 0)

Equation of line using two point slope form .

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

(x_1,y_1)=(0,7)

(x_2,y_2)=(7,0)

Substitute values in formula :

$y-7=\frac{0-7}{`7-0}(x-0)$

$y-7=\frac{-7}{7}(x)$

y= -x+7

Option D: (0, 7) and (3, 0)

Equation of line using two point slope form .

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

(x_1,y_1)=(0,7)

(x_2,y_2)=(3,0)

Substitute values in formula :

$y-7=\frac{0-7}{`3-0}(x-0)$

$y-7=\frac{-7}{3}(x)$

$y=\frac{-7}{3}(x)+7$

Now after plotting all the lines of given options on the graph of scatter plot we can see that the blue line $y=\frac{-13}{10}x+14$ of Option B the is the line of best fit for this scatter plot Since it is covering almost all ordered pairs of scatter plot.

Hence two ordered pairs can be joined to best draw the line of best fit for this scatter plot are (0, 14) and (10, 1)

Option B is correct.

Ascatter plot is shown below: a graph shows numbers from 0 to 10 on the x axis at increments of 1 a

Answer from: Quest

$a_1 = 1$ , and

$a_{n+1} = a_n + (n + 1)$ for $n \ge 1$

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote $a_1 = 1$ , $a_2 = 3$ , $a_3 = 6$ , so that we can call

1 the 1st term, 3 the 2nd term, 6 the 3rd term,etc.

note the following:

from the 1st term (1) to the 2nd term (3), we go up by 2,from the 2nd term (3) to the 3rd term (6), we go up by 3from the 3rd term (6) to the 4th term (10), we go up by 4, andfrom the 4th term (10) to the 5th term (15), we go up by 5.

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from $a_1 = 1$ , to get to $a_2 = 3$ , we add $2(=1+1)$