Question

What is the slope of the line of the best fit for this scatter plot?

What is the equation of the line of the best fit?

Answer 1

see explanation

Explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Calculate m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (2, 7) and (x₂, y₂ ) = (4, 6) ← 2 points on the line

m =
`(6-7)/(4-2)` = -
`(1)/(2)`

Note the line crosses the y- axis at (0, 8) ⇒ c = 8

y = -
`(1)/(2)` x + 8 ← equation of line

Answer 2

Answer : The slope of the line and equation of the line is,
`(-1)/(2)` and
`y=(-1)/(2)x+8` respectively.

Step-by-step explanation :

The general form for the formation of a linear equation is:

`(y-y_1)=m* (x-x_1)` .............(1)

where,

x and y are the coordinates of x-axis and y-axis respectively.

m is slope of line.

First we have to calculate the slope of line.

Formula used :

`m=((y_2-y_1))/((x_2-x_1))`

Here,

`(x_1,y_1)=(2,7)` and
`(x_2,y_2)=(4,6)`

`m=((6-7))/(4-2))`

`m=(-1)/(2)`

Now put the value of slope in equation 1, we get the linear equation.

`(y-y_1)=m* (x-x_1)`

`(y-7)=(-1)/(2)* (x-2)`

`y-7=(-1)/(2)x+1`

`y=(-1)/(2)x+1+7`

`y=(-1)/(2)x+8`

Thus, the slope of the line and equation of the line is,
`(-1)/(2)` and
`y=(-1)/(2)x+8` respectively.