If $$ f(x) $$ is a linear function and given $$ f(7)=-6 $$ and $$ f(9)=5 $$, determine the linear function. a.) What is the slope? (Be sure to leave your answer in reduced fraction form.) b.) What is the $$ y $$-intercept? fraction form.) c.) What is $$ f(x) $$ ? $$ f(x)= $$

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**Step 1. Calculate the Slope**

Given two points $$ (7, -6) $$ and $$ (9, 5) $$, the slope $$ m $$ is calculated by  
$$
m = \frac{5 - (-6)}{9 - 7} = \frac{5 + 6}{2} = \frac{11}{2}.
$$

**Step 2. Determine the $$ y $$-intercept**

The linear function has the form  
$$
f(x)=mx+b.
$$
Using the point $$ (7, -6) $$ and $$ m=\frac{11}{2} $$, we substitute to find $$ b $$:
$$
-6 = \frac{11}{2} \times 7 + b.
$$
Calculate $$ \frac{11}{2} \times 7 $$:
$$
\frac{11 \cdot 7}{2} = \frac{77}{2}.
$$
Now solve for $$ b $$:
$$
b = -6 - \frac{77}{2}.
$$
Convert $$-6$$ to a fraction with denominator 2:
$$
-6 = -\frac{12}{2},
$$
so
$$
b = -\frac{12}{2} - \frac{77}{2} = -\frac{89}{2}.
$$

**Step 3. Write the Linear Function**

Now substitute $$ m=\frac{11}{2} $$ and $$ b=-\frac{89}{2} $$ into the function:
$$
f(x)=\frac{11}{2}x - \frac{89}{2}.
$$
**a.) Slope:** $$ \frac{11}{2} $$ **b.) $$ y $$-intercept:** $$ -\frac{89}{2} $$ **c.) Linear Function:** $$ f(x) = \frac{11}{2}x - \frac{89}{2} $$

If is a linear function and given and , determine the linear function.
a.) What is the slope? (Be sure to leave your answer in reduced fraction
form.)
b.) What is the -intercept?
fraction form.)
c.) What is ?

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If is a linear function and given and , determine the linear function. a.) What is the slope? (Be sure to leave your answer in reduced fraction form.) b.) What is the -intercept? fraction form.) c.) What is ?