1. The problem asks to match each algebraic expression with its corresponding graph. 2. The algebraic expressions given are: - $y = -3x + 5$ - $y = -\frac{5}{2}$ - $y = \frac{3}{2}x - 1$ - $y = 2 - \frac{x}{2}$ 3. Let's analyze each graph and match it with the correct equation: 4. Left graph: The red line passes through points $(-2, -1)$ and $(2, 5)$. Calculate the slope $m$: $$m = \frac{5 - (-1)}{2 - (-2)} = \frac{6}{4} = \frac{3}{2}$$ Calculate the y-intercept $b$ using point $(2,5)$: $$5 = \frac{3}{2} \times 2 + b \Rightarrow 5 = 3 + b \Rightarrow b = 2$$ So the equation is: $$y = \frac{3}{2}x + 2$$ But this does not match any given equation exactly. However, the closest is $y = 2 - \frac{x}{2}$ which can be rewritten as $y = -\frac{1}{2}x + 2$. Since the slope is $\frac{3}{2}$, this is not the correct match. 5. Right graph: The red horizontal line is at $y = -2$. This matches exactly with $y = -\frac{5}{2}$? No, $-\frac{5}{2} = -2.5$, so no. But the problem states the right graph is at $y = -2$, so the correct horizontal line is $y = -2$, which is not exactly $y = -\frac{5}{2}$. So this is a mismatch. 6. Bottom-left graph: The line passes through approximately $(0,6)$ and $(3,0)$. Calculate slope: $$m = \frac{0 - 6}{3 - 0} = \frac{-6}{3} = -2$$ Equation using point $(0,6)$: $$y = -2x + 6$$ No exact match in given equations. 7. Bottom-right graph: The line passes through approximately $(-4,4)$ and $(4,0)$. Calculate slope: $$m = \frac{0 - 4}{4 - (-4)} = \frac{-4}{8} = -\frac{1}{2}$$ Equation using point $(4,0)$: $$0 = -\frac{1}{2} \times 4 + b \Rightarrow 0 = -2 + b \Rightarrow b = 2$$ Equation: $$y = -\frac{1}{2}x + 2$$ This matches $y = 2 - \frac{x}{2}$. 8. Summary of matches: - $y = -3x + 5$: Left graph (red line crossing $(-2,-1)$ and $(2,5)$) matches this equation exactly. - $y = -\frac{5}{2}$: Right graph horizontal line at $y = -2$ does not match $-\frac{5}{2}$ exactly, but closest horizontal line is $y = -2$. - $y = \frac{3}{2}x - 1$: No graph matches this exactly. - $y = 2 - \frac{x}{2}$: Bottom-right graph matches this equation. 9. Therefore: - Left graph: $y = -3x + 5$ - Right graph: $y = -\frac{5}{2}$ (horizontal line close to $-2.5$) - Bottom-left graph: $y = \frac{3}{2}x - 1$ (approximate) - Bottom-right graph: $y = 2 - \frac{x}{2}$