Question: c 1.3 Question: Skills 1.3.A.1 and 1.3.A.3 The table below gives values of f(x) for selected values of x: x -5 1 4 f(x) -12 -4 0 Let f(x) is a linear function. What is the value of f(10)?

1. **State the problem:** We are given a linear function $f(x)$ with values at $x=-5, 1, 4$ and corresponding $f(x)$ values $-12, -4, 0$. We need to find $f(10)$. 2. **Recall the formula for a linear function:** A linear function can be written as $$f(x) = mx + b$$ where $m$ is the slope and $b$ is the y-intercept. 3. **Calculate the slope $m$ using two points:** Use points $(1, -4)$ and $(4, 0)$. $$m = \frac{f(4) - f(1)}{4 - 1} = \frac{0 - (-4)}{4 - 1} = \frac{4}{3}$$ 4. **Find the y-intercept $b$:** Use point $(1, -4)$ and slope $m=\frac{4}{3}$. $$-4 = \frac{4}{3} \times 1 + b \implies b = -4 - \frac{4}{3} = -\frac{12}{3} - \frac{4}{3} = -\frac{16}{3}$$ 5. **Write the function:** $$f(x) = \frac{4}{3}x - \frac{16}{3}$$ 6. **Calculate $f(10)$:** $$f(10) = \frac{4}{3} \times 10 - \frac{16}{3} = \frac{40}{3} - \frac{16}{3} = \frac{24}{3} = 8$$ **Final answer:** $$f(10) = 8$$