step by step solution-:

To find the equation for shoe size and foot length and calculate the size for the foot of length 9.5 inches:

The given scenario is a linear function in nature:

Let x be the foot length of the men’s shoe and let y be the size of the men’s shoe.

Apply slope formula:

m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}

Substitute coordinates of points (10,{\frac{15}{2}}) and (11, {\frac{23}{2}}) into the **slope formula**:

m=\frac{\textcolor{primary}{\frac{23}{2}}-\textcolor{primary}{\frac{15}{2}}}{\textcolor{secondary}{11}-\textcolor{secondary}{10}}

After simplifying we get,

m=4

linear Equation of line is:

(y-y_{1})=m\cdot(x-x_{1})

Substitute coordinates of points (10,15/2) and m=4 into the above formula.

(y-\frac{15}{2})=4\cdot(x-10)

After simplifying we get,

8x-2y=65

Clothing men’s shoe size are a linear function of foot is:

8x-2y=65

Substitute the x=9.5 into the above,

8\times9.5-2y=65

After simplifying we get,

y=5.5

The required shoe size is 5.5.

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