1. **State the problem:** We have two linear relationships: - Relationship R: $$0.2x - 0.01y = 0.03$$ - Relationship W: given by points $(x, y)$ in the table: $-2, -18$, $-1, -13$, $0, -8$, $1, -3$, $2, 2$. We need to find the slope and y-intercept of both relationships and verify the statements about which has the largest slope and y-intercept, and the behavior of relationship W as $$x \to \infty$$. 2. **Find slope and y-intercept of relationship R:** Start with the equation: $$0.2x - 0.01y = 0.03$$ Solve for $$y$$: $$-0.01y = 0.03 - 0.2x$$ $$y = \frac{0.03 - 0.2x}{-0.01}$$ Divide numerator and denominator: $$y = \frac{0.03}{-0.01} - \frac{0.2x}{-0.01}$$ $$y = -3 + 20x$$ So, the slope $$m_R = 20$$ and the y-intercept $$b_R = -3$$. 3. **Find slope and y-intercept of relationship W:** Use two points from the table, for example $(x_1, y_1) = (-2, -18)$ and $(x_2, y_2) = (-1, -13)$. Slope formula: $$m_W = \frac{y_2 - y_1}{x_2 - x_1} = \frac{-13 - (-18)}{-1 - (-2)} = \frac{5}{1} = 5$$ Use point-slope form to find y-intercept $$b_W$$ using point $(0, -8)$: $$y = mx + b$$ $$-8 = 5 \times 0 + b$$ $$b = -8$$ So, slope $$m_W = 5$$ and y-intercept $$b_W = -8$$. 4. **Compare slopes and y-intercepts:** - $$m_R = 20$$ vs $$m_W = 5$$, so relationship R has the larger slope. - $$b_R = -3$$ vs $$b_W = -8$$, so relationship R has the larger y-intercept. 5. **Behavior as $$x \to \infty$$ for relationship W:** Since $$m_W = 5 > 0$$, as $$x \to \infty$$, $$y = 5x - 8 \to \infty$$. **Final answers:** - Linear relationship R has the largest slope. - Linear relationship R has the largest y-intercept. - As $$x \to \infty$$, $$y \to \infty$$ for linear relationship W.