Answer
The linear function obtained is $f\left( x \right)=-2.36x+254.84$.
Work Step by Step
Locate any two points in the line and use them to calculate the slope of the linear function as follows:
The two points of the line are $\left( {{x}_{1}},{{y}_{1}} \right)=\left( 19,210 \right)$ and $\left( {{x}_{2}},{{y}_{2}} \right)=\left( 74,80 \right)$.
Obtain the value of slope (m) using the formula given below:
$\begin{align}
& m=\frac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}} \\
& =\frac{80-210}{74-19} \\
& =-2.36
\end{align}$
Now, substitute the slope in the line equation as follows:
$\begin{align}
& \left( y-{{y}_{1}} \right)=m\left( x-{{x}_{1}} \right) \\
& \left( y-210 \right)=-2.36\left( x-19 \right) \\
& \left( y-210 \right)=-2.36x+44.84 \\
& y+2.36x=254.84
\end{align}$
So, the function obtained is $f\left( x \right)=-2.36x+254.84$.
The slope of the function is defined as the change in y per unit change in the x coordinate. That means that for every unit change in $x$, $y$ decreases by $2.36$ units.
Here, $y$ is the child mortality rate (children aged under 5) and $x$ is the percentage of female adults who are literate. So, for every $1$ unit percentage increase of literacy in women, the child mortality decreases by 2.36.
Hence, the function of the given data is $f\left( x \right)=-2.36x+254.84$ and for every $1$ unit percentage increase of literacy in woman, the child mortality decreases by 2.36.
