1. **State the problem:** We are given two functions: Function 1 represented by points on a graph and Function 2 represented by a table of values. We need to determine which statement about their slopes and y-intercepts is true. 2. **Find the slope and y-intercept of Function 1:** - From the graph, two points on Function 1 are $(-1, -4)$ and $(2, 3)$. - The slope formula is $$m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{3 - (-4)}{2 - (-1)} = \frac{7}{3}.$$ - To find the y-intercept, use point-slope form with point $(2,3)$: $$y = mx + b \Rightarrow 3 = \frac{7}{3} \times 2 + b \Rightarrow 3 = \frac{14}{3} + b.$$ - Solve for $b$: $$b = 3 - \frac{14}{3} = \frac{9}{3} - \frac{14}{3} = -\frac{5}{3}.$$ 3. **Find the slope and y-intercept of Function 2:** - From the table, points are $(-2,1)$ and $(-1,8)$. - Calculate slope: $$m = \frac{8 - 1}{-1 - (-2)} = \frac{7}{1} = 7.$$ - Find y-intercept by using point $(-2,1)$: $$1 = 7 \times (-2) + b \Rightarrow 1 = -14 + b.$$ - Solve for $b$: $$b = 1 + 14 = 15.$$ 4. **Compare slopes and y-intercepts:** - Function 1 slope: $\frac{7}{3} \approx 2.33$; y-intercept: $-\frac{5}{3} \approx -1.67$. - Function 2 slope: $7$; y-intercept: $15$. - Function 1 has a smaller slope and smaller y-intercept than Function 2. 5. **Conclusion:** The correct statement is: C. Function 1 has a smaller slope and y-intercept than Function 2.