In Part A, we drew the following line of best fit.

Let's write an equation in slope-intercept form for this line!

y = m x + b

In this equation,

m

is the slope and

b

is the

y -

intercept. First, we will choose any two points on the line.

The first point has coordinates

x_{1} = 70

and

y_{1} = 70.8 .

The second point has coordinates

x_{2} = 80

and

y_{2} = 73.7 .

Let's substitute these values into slope formula.

m = \frac{y _{2} - y _{1}}{x _{2} - x _{1}}

Substitute values

m = \frac{7 3 . 7 - 7 0 . 8}{8 0 - 7 0}

Subtract terms

m = \frac{2 . 9}{1 0}

Calculate quotient

m = 0.29

We found that the slope

m

is equal to

0.29 .

This means that the life expectancy of a person born in a certain year is longer by

0.29

years than the life expectancy of a person born in a previous year.

y = m x + b \Leftrightarrow y = 0.29 + b

The

y -

intercept

b

is the

y -

value when

x = 0 .

We can find it on the graph. Let's do it!

We can see that the

y -

intercept is equal to about

50 .

This means that in the year

1900,

the life expectancy was approximately equal to

50

years. Finally, we can write a complete equation in slope-intercept form for our line of fit.

y = 0.29 x + b ⇕ y = 0.29 x + 50

Exercise