Q54. - Algebra 2

Question

Use the table that shows the life expectancy for people born in various years.

Find the prediction equation.

Step-by-Step Solution

Answer

The prediction equation of life expectancy of a person is $y=0.18x+67.9$

Step-1 – Determine the given value.

Consider year as x coordinate and expectancy as y coordinate.

Also consider 1950 as the 0 because the life expectancy in the table starts from 1950.

 We have data of people born in various years.

$\backslash \left[\right(0,68.2)\backslash ]\backslash \left[\right(10,69.7)\backslash ]\backslash \left[\right(20,70.8)\backslash ]\backslash \left[\right(30,73.7)\backslash ]\backslash \left[\right(40,75.4)\backslash ]\backslash \left[\right(47,76.5)\backslash ]$

Step-3 – Determine the slope.

Use the point $(10,69.7)$ and $(47,76.5)$to find the slope

$\begin{array}{l}m=\frac{y_2-y_1}{x_2-x_1}\\ m=\frac{76.5-69.7}{47-10}\\ m=\frac{6.8}{37}\\ m=0.18\end{array}$

Step-4 – Determine the equation.

Use the point-slope form 

$\begin{array}{l}y-y_1=m(x-x_1)\\ y-69.7=0.18(x-10)\\ y-69.7=0.18x-1.8\\ y=0.18x+67.9\end{array}$