Answer
See below:
Work Step by Step
(a)
The line cuts the \[y\]-axis at the point,\[\left( 0,254 \right)\].
So, the \[y\]-intercept is,\[254\].
The y-intercept of the graph interprets that if none of the adult females are literate then the mortality rate of children under five would be \[254\] per thousand.
(b)
The slope of a line passing through two points \[\left( {{x}_{1}},{{y}_{1}} \right)\] and \[\left( {{x}_{2}},{{y}_{2}} \right)\] can be calculated by formula change in \[y\] axis divided by change in \[x\] axis as,
\[\frac{\Delta y}{\Delta x}=\frac{254-110}{0-60}=-2.4\]
The slope of the graph interprets that for each \[1%\] of adult females who are literate corresponding to which the mortality rate of children under \[5\] decreases by \[2.4\]per thousand.
Hence, the slope is \[-2.4\] and it describes that for each \[1%\] of adult females who are literate corresponding to which the mortality rate of children under \[5\] decreases by \[2.4\]per thousand.
(c)
As from part (a) the \[y\]-intercept is \[254\] and from part (b) the slope is \[-2.4\].
Use the equation use of\[y=mx+c\], where \[m\]is the slope and \[c\] is the \[y\]-intercept to determine the equation of the graph by substituting the values of slope and \[y\]-intercept in the slope-intercept equation.
Thus,
\[f\left( x \right)=y=-2.4x+254\]
Hence, the linear function of the provided graph is, \[f\left( x \right)=-2.4x+254\].
(d)
Use the function from part (c) that is \[f\left( x \right)=-2.4x+254\], that models child mortality, f(x), per thousand, for children under five in a country where \[x%\] of adult women are literate.
For\[x=50\]
\[\begin{align}
& f\left( 50 \right)=-2.4\cdot 50+254 \\
& =-120+254 \\
& =134
\end{align}\]
The mortality rate of children under five in a country is \[134\] per thousand when\[50%\] of adult females are literate.
