1. **State the problem:** We are given a table of values for a function $f(x)$ at points $x=0,1,2,3,4$ with corresponding values $f(x)=-1,-7,-13,-19,-25$. We want to find the formula for $f(x)$. 2. **Identify the pattern:** Notice the values decrease by 6 each time: $-7 - (-1) = -6$, $-13 - (-7) = -6$, etc. This suggests a linear function of the form $$f(x) = mx + b$$ where $m$ is the slope. 3. **Calculate the slope $m$:** Using two points, for example $(0,-1)$ and $(1,-7)$, $$m = \frac{f(1) - f(0)}{1 - 0} = \frac{-7 - (-1)}{1} = \frac{-6}{1} = -6$$ 4. **Find the intercept $b$:** Since $f(0) = -1$, substituting into $f(x) = -6x + b$ gives $$-1 = -6 \times 0 + b \implies b = -1$$ 5. **Write the formula:** $$f(x) = -6x - 1$$ 6. **Verify with another point:** For $x=2$, $$f(2) = -6 \times 2 - 1 = -12 - 1 = -13$$ which matches the table. **Final answer:** $$f(x) = -6x - 1$$