1. **Stating the problem:** We have two taps flowing simultaneously. One tap flows at 10 ml/s, the other at 20 ml/s. 2. **Identifying the graphs:** Graph A reaches 20 ml at 6 seconds, so its flow rate is $\frac{20}{6} \approx 3.33$ ml/s, but since the problem states 20 ml/s, the graph must be linear and the point at 6 seconds is 20 ml, so the flow rate is $\frac{20}{6} = 3.33$ ml/s which contradicts the problem. Actually, the problem states the flow rates directly: 10 ml/s and 20 ml/s. 3. **Correct interpretation:** Graph A reaches 20 ml at 1 second (since 20 ml/s), so at 6 seconds it should be $20 \times 6 = 120$ ml, but the graph shows 20 ml at 6 seconds, so the graph labeled A corresponds to 20 ml total at 6 seconds, so flow rate is $\frac{20}{6} \approx 3.33$ ml/s. Similarly, graph B reaches 10 ml at 6 seconds, so flow rate is $\frac{10}{6} \approx 1.67$ ml/s. This contradicts the problem statement, so the graphs must be interpreted as follows: - Graph A corresponds to 20 ml/s flow rate. - Graph B corresponds to 10 ml/s flow rate. 4. **Answer for part a:** - Graph A corresponds to 20 ml/s. - Graph B corresponds to 10 ml/s. 5. **Answer for part b:** The vertical axis values should be labeled as 0, 10, 20 milliliters. --- 6. **Problem 5: Function $y=12x-6$** **a)** Find $y$ when $x=1.5$: $$y=12 \times 1.5 - 6 = 18 - 6 = 12$$ **b)** Find $x$ when $y=72$: $$72 = 12x - 6$$ $$72 + 6 = 12x$$ $$78 = 12x$$ $$x = \frac{78}{12} = 6.5$$ **c)** Find $x$-intercept (where $y=0$): $$0 = 12x - 6$$ $$6 = 12x$$ $$x = \frac{6}{12} = 0.5$$ **d)** Find intersection with $y=11x-5$: Set equal: $$12x - 6 = 11x - 5$$ $$12x - 11x = -5 + 6$$ $$x = 1$$ Find $y$: $$y = 12 \times 1 - 6 = 6$$ Intersection point is $(1,6)$. **e)** Find $x$ values where $y<0$: $$12x - 6 < 0$$ $$12x < 6$$ $$x < \frac{6}{12} = 0.5$$ **f)** Check if point $B(-50, -605)$ lies on graph: Calculate $y$ for $x=-50$: $$y = 12 \times (-50) - 6 = -600 - 6 = -606$$ Since $-606 \neq -605$, point B does not lie on the graph. **g)** Find formula of line through $D(2,25)$ parallel to $y=12x-6$: Parallel lines have same slope $m=12$. Use point-slope form: $$y - 25 = 12(x - 2)$$ $$y = 12x - 24 + 25 = 12x + 1$$ **Final answers:** - a) $y=12$ - b) $x=6.5$ - c) $x=0.5$ - d) Intersection at $(1,6)$ - e) $x<0.5$ - f) No, point B is not on the graph - g) $y=12x+1$