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On pose f(x)=ax+b. Calculer a et donner la valeur de b 

To calculate the values of \( a \) and \( b \) for the affine function \( f(x) = ax + b \), we can use the table of values provided.

From the table:

\[
\begin{array}{c|c|c|c|c|c|c|c|c|c}
x & 0 & 2 & 4 & 6 & 8 & 10 & 12 & 14 \\
\hline
f(x) & 2 & -8 & -18 & -28 & -38 & -48 & -58 & -68 \\
\end{array}
\]

### Step 1: Find the slope \( a \)
Since the function \( f(x) \) is affine, the slope \( a \) is constant. We can calculate \( a \) using two points, say \( (x_1, f(x_1)) \) and \( (x_2, f(x_2)) \).

Take the points \( (0, 2) \) and \( (2, -8) \):
\[
a = \frac{f(x_2) - f(x_1)}{x_2 - x_1} = \frac{-8 - 2}{2 - 0} = \frac{-10}{2} = -5
\]
Thus, \( a = -5 \).

### Step 2: Find \( b \)
Using the fact that \( f(x) = ax + b \), we can substitute one of the known points to solve for \( b \).

Using the point \( (0, 2) \):
\[
f(0) = a(0) + b = 2
\]
\[
b = 2
\]

### Final result:
The affine function is \( f(x) = -5x + 2 \).

Would you like more details or further clarification?

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Here are 5 related questions you can explore:

1. How do you verify the correctness of \( f(x) = -5x + 2 \) using the other points in the table?
2. Can you graph the function \( f(x) = -5x + 2 \) and identify its key features?
3. What is the geometric interpretation of the slope \( a \) and intercept \( b \)?
4. How would the function change if \( a \) were positive instead of negative?
5. Can you derive a similar function \( g(x) \) from the given problem?

**Tip:** When finding the slope of an affine function, you only need two points, but checking with multiple points ensures accuracy.

On pose f(x)=ax+b. Calculer a et donner la valeur de b

Learn how to calculate the slope (a) and intercept (b) for the affine function f(x) = ax + b using a table of values. Step-by-step solution provided. Suitable for students in Grades 8-10.

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