1. **State the problem:** We have four linear functions and need to answer three questions about their y-intercepts and slopes. 2. **Identify y-intercepts and slopes:** - Function 1: Graph not fully described, but it is a line descending from left to right, so slope is negative. Y-intercept is not given explicitly. - Function 2: Given table of points. To find slope $m$, use two points, e.g., $(x_1,y_1)=(-2,-13)$ and $(x_2,y_2)=(-1,-8)$: $$m=\frac{y_2 - y_1}{x_2 - x_1} = \frac{-8 - (-13)}{-1 - (-2)} = \frac{5}{1} = 5$$ To find y-intercept $b$, use point $(0,-3)$: $$y = mx + b \Rightarrow -3 = 5 \times 0 + b \Rightarrow b = -3$$ - Function 3: Equation given as $y = -4x + 4$, so slope $m = -4$, y-intercept $b = 4$. - Function 4: Slope $m = 2$, y-intercept $b = 1$. 3. **Answer (a): Which function has y-intercept closest to 0?** - Function 1: Unknown. - Function 2: $b = -3$ (distance from 0 is 3). - Function 3: $b = 4$ (distance 4). - Function 4: $b = 1$ (distance 1). Closest to 0 is Function 4. 4. **Answer (b): Which function has greatest slope?** - Function 1: Negative slope. - Function 2: $m=5$. - Function 3: $m=-4$. - Function 4: $m=2$. Greatest slope is Function 2. 5. **Answer (c): Which functions have y-intercepts greater than 3?** - Function 1: Unknown. - Function 2: $b=-3$ (not greater than 3). - Function 3: $b=4$ (greater than 3). - Function 4: $b=1$ (not greater than 3). Only Function 3 has y-intercept greater than 3. **Final answers:** (a) Function 4 (b) Function 2 (c) Function 3