Answer
$w=6h+106$
Work Step by Step
Let $w$ be the weight in pounds and $h$ be the height in inches above $5$ feet. A linear equation that gives the optimal weight of men based on the number of inches above $5$ feet takes the form of
$$
w=mh+b,
$$
where $m$ is the slope and $b$ is the $y$-intercept.
Since the optimal weight at $5$ feet (i.e. $0$ inches more than $5$ feet) is $106$ pounds, this can be represented by the ordered pair $(h_1,w_1)=(0,106)$. Since the optimal weight at $5.5$ feet (i.e. $6$ inches more than $5$ feet) is $142$ pounds, this can be represented by the ordered pair $(h_2,w_2)=(6,142)$.
The formula for finding the slope, $m$, of the line passing through two points, $(h_1,w_1)$ and $(h_2,w_2)$ is given by $m=\frac{w_1-w_2}{h_1-h_2}$. That is,
$$\begin{aligned}
m&=\frac{w_1-w_2}{h_1-h_2}
\\&=
\frac{106-142}{0-6}
\\&=
\frac{-36}{-6}
\\&=
6
.\end{aligned}
$$With $m=6$, then the linear equation that gives the optimal weight of men based on the number of inches above $5$ feet takes the form of
$$
w=6h+b
.$$Since the line passes through the point $(0,106)$, substitute $h=0$ and $w=106$ in the equation above to solve for $b$. That is,
$$\begin{aligned}
w&=6h+b
\\
106&=6(0)+b
\\
106&=b
.\end{aligned}
$$With $b=106$, then the linear equation that gives the optimal weight of men based on the number of inches above $5$ feet is
$$
w=6h+106
.$$
