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Let's analyze and solve the given problem step by step.

### Given function:
\[ f(x) = 7x - 2 \]

#### (a) Evaluate \( f(-1) \)
To find \( f(-1) \), substitute \( x = -1 \) into the function:

\[
f(-1) = 7(-1) - 2 = -7 - 2 = -9
\]

So, \( f(-1) = -9 \).

#### (b) Find the value of \( p \) when \( f(p) = -30 \)
We are given that:
\[
f(p) = -30
\]

Substitute the expression for \( f(x) \) into this equation:

\[
7p - 2 = -30
\]

Now, solve for \( p \):

\[
7p = -30 + 2
\]
\[
7p = -28
\]
\[
p = \frac{-28}{7} = -4
\]

So, \( p = -4 \).

### Final Answers:
- \( f(-1) = -9 \)
- \( p = -4 \)

Would you like more details on any step or further explanation? Here are 5 related questions to expand your understanding:

1. How can we find the inverse of the function \( f(x) = 7x - 2 \)?
2. What does the slope of the function \( f(x) = 7x - 2 \) represent geometrically?
3. Can you explain how changes in \( f(x) \)'s slope or intercept affect the graph?
4. How would you find the value of \( f(x) \) for a given \( x \) on the graph?
5. What other transformations could we apply to this function to shift its graph?

**Tip**: Always substitute values carefully in algebraic functions to avoid small mistakes in arithmetic!

A function f(x) is defined by f(x) = 7x - 2.
(a) Evaluate f(-1).
(b) f(p) = -30. Calculate the value of p.

Learn how to evaluate the function f(x) = 7x - 2 for specific values, and solve for p when f(p) = -30. This problem covers key algebraic concepts in function evaluation and linear equations, suitable for students in Grades 7-9.

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