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(a)

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Equation for the family of linear functions is $\"\"$ .

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Where $\"\"$ slope and $\"\"$ intercept.

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Here slope $\"\"$ .

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The linear function is $\"\"$ .

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Graph :

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Draw a family of lines $\"\"$ , assume the values of $\"\"$ are $\"\"$ .

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$\"\"$

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(b)

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Equation for the family of linear functions is $\"\"$ .

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Given $\"\"$ it means that $\"\"$ and $\"\"$ .

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Find the relation for $\"\"$ :

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The linear function is $\"\"$ .

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Substitute $\"\"$ and $\"\"$ in the above equation.

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$\"\"$

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Now substitute $\"\"$ in the family of linear functions.

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Then the equation of the family of linear functions is $\"\"$ .

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Graph :

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Draw the equation of the family of linear functions is $\"\"$ .

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If $\"\"$ then $\"\"$ .

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If $\"\"$ then $\"\"$ .

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If $\"\"$ then $\"\"$ .

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If $\"\"$ then $\"\"$ .

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$\"\"$

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(c)

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Find the function belongs to both families.

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Use the line equation from part (b) and slope from part (a).

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The equation is $\"\"$ and slope is $\"\"$ .

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Substitute $\"\"$ in $\"\"$

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$\"\"$

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$\"\"$

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The function $\"\"$ belongs to both families.

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(a) $\"\"$ , where $\"\"$ intercept.

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$\"\"$

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(b) $\"\"$ , where $\"\"$ slope.

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$\"\"$

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(c) $\"\"$ .