Question

A scatter 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)

Answer 1

The answer is B: (0, 14) and (10, 1)

Explanation:

Answer 2

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

Explanation:

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

Equation of line using two point slope form .

`y-y_1=(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=(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=(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=(1-14)/(`10-0)(x-0)`

`y-14=(-13)/(10)(x-0)`

`y=(-13)/(10)x+14`

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

Equation of line using two point slope form .

`y-y_1=(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=(0-7)/(`7-0)(x-0)`

`y-7=(-7)/(7)(x)`

`y= -x+7`

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

Equation of line using two point slope form .

`y-y_1=(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=(0-7)/(`3-0)(x-0)`

`y-7=(-7)/(3)(x)`

`y=(-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=(-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.