1. **State the problem:** We are given two functions: $$y = \frac{|x+5|}{4}$$ and $$y = 2x - 3$$ We need to complete the table for given values of $x$ by calculating $y$ for both functions. 2. **Recall the formulas:** - For the absolute value function: $$y = \frac{|x+5|}{4}$$ - For the linear function: $$y = 2x - 3$$ 3. **Calculate values for each $x$:** - For $x = -9$: - $$y = \frac{|-9+5|}{4} = \frac{|-4|}{4} = \frac{4}{4} = 1$$ - $$y = 2(-9) - 3 = -18 - 3 = -21$$ - For $x = -1$: - $$y = \frac{|-1+5|}{4} = \frac{|4|}{4} = \frac{4}{4} = 1$$ - $$y = 2(-1) - 3 = -2 - 3 = -5$$ - For $x = 3$: - $$y = \frac{|3+5|}{4} = \frac{|8|}{4} = \frac{8}{4} = 2$$ - $$y = 2(3) - 3 = 6 - 3 = 3$$ 4. **Interpretation:** - The absolute value function creates a V-shaped graph with vertex at $(-5,0)$, opening upwards and scaled by $\frac{1}{4}$. - The linear function is a straight line with slope 2 and y-intercept -3. 5. **Final completed table:** | x | $\frac{|x+5|}{4}$ | $2x-3$ | |------|-------------------|-----------| | -9 | 1 | -21 | | -1 | 1 | -5 | | 3 | 2 | 3 |