Question

Shannon drew the line of best fit on the scatter plot shown below:

A graph is shown with scale along x axis from 0 to 10 at increments of 1 and scale along y axis from 0 to 15 at increments of 1.The ordered pairs 0, 14 and 1, 13.1 and 2, 12 and 3, 10 and 4, 8.5 and 5, 7 and 5.6, 6 and 6, 4.9 and 7, 3.4 and 8, 2.9 and 9, 2 and 9.5, 0.5 are shown on the graph. A straight line joins the ordered pairs 0,14 and 10, 0.

What is the approximate equation of this line of best fit in slope-intercept form?
A y = negative 7 over 5x + 14
B y = −14x + 7 over 5
C y = negative 5 over 7x + 14
D y = −14x + 5 over 7

Answer 1

The approximate equation of this line of best fit in slope-intercept form is:

`y=(-7)/(5)* x+14`

( i.e. option A is correct ; y = negative 7 over 5 x + 14 )

Explanation:

Shannon drew the line of best fit on the scatter plot based on the information provided to us.

He observes that a straight line i.e. the line of best fit joins the ordered pairs (0,14) and (10,0).

Now we are asked to find the approximate equation of this line of best fit in slope-intercept form.

We know that the slope intercept form of a line is given by:

`y=mx+c` where m denotes the slope of the line and c denote the y-intercept.

Also we know that the equation of a line passing through two points (a,b) and (c,d) is given by:

`y-b=(d-b)/(c-a)* (x-a)`

Here we have:

(a,b)=(0,14) and (c,d)=(10,0).

So equation of line is:

`y-14=(0-14)/(10-0)* (x-0)\\\\y-14=(-14)/(10)* x\\\\y-14=(-7)/(5)* x\\\\y=(-7)/(5)* x+14`

Hence, the approximate equation of this line of best fit in slope-intercept form is:

`y=(-7)/(5)* x+14`

( i.e. option A is correct ; y = negative 7 over 5 x + 14 )

Answer 2

y-intercept of line is 14
slope of line = (0 - 14)/(10 - 0) = -14/10 = -7/5

Required equation is y = -7/5 x + 14