fhe function $$ f $$ is defined by the given equation, where $$ b $$ and $$ c $$ are constants. The graph The foriew of $$ y=f(x) $$ in the $$ x y $$-plane passes through the points $$ (0,6) $$ and $$ (8,0) $$. What is the value of $$ b $$ ?

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To find the value of $$ b $$ in the function $$ f $$, we need to analyze the information given about the points through which the graph passes.

1. **Extract Known Conditions:**
   - The function $$ f $$ passes through the points $$ (0, 6) $$ and $$ (8, 0) $$.
   - This means that:
     - $$ f(0) = 6 $$
     - $$ f(8) = 0 $$

2. **Assume a Form for the Function:**
   - Since we don't have the explicit form of the function $$ f $$, we can assume it is a linear function of the form:
     $$
     f(x) = mx + c
     $$
   - Here, $$ m $$ is the slope and $$ c $$ is the y-intercept.

3. **Use the Points to Set Up Equations:**
   - From the point $$ (0, 6) $$:
     $$
     f(0) = c = 6
     $$
   - From the point $$ (8, 0) $$:
     $$
     f(8) = 8m + c = 0
     $$
   - Substituting $$ c = 6 $$ into the second equation:
     $$
     8m + 6 = 0
     $$

4. **Solve for $$ m $$:**
   - Rearranging the equation gives:
     $$
     8m = -6 \implies m = -\frac{6}{8} = -\frac{3}{4}
     $$

5. **Write the Function:**
   - Now we can write the function:
     $$
     f(x) = -\frac{3}{4}x + 6
     $$

6. **Identify Constants $$ b $$ and $$ c $$:**
   - In this case, if we assume $$ b $$ corresponds to the slope $$ m $$, then:
     $$
     b = -\frac{3}{4}
     $$

Thus, the value of $$ b $$ is $$-\frac{3}{4}$$.
The value of $$ b $$ is $$-\frac{3}{4}$$.

fhe function is defined by the given equation, where and are constants. The graph
The foriew
of in the -plane passes through the points and . What is the value
of ?

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fhe function is defined by the given equation, where and are constants. The graph The foriew of in the -plane passes through the points and . What is the value of ?