1. The problem asks us to match each linear equation to the graph based on the points shown. 2. The equations are: a) $y = 5x$ b) $y = -2x + 3$ c) $y = 4x + 6$ 3. The graph shows points approximately at $(-2, 10)$, $(-1, 6)$, $(0, 2)$, $(1, -2)$, and $(2, -6)$. 4. To match, we check which equation fits these points by substituting the $x$ values and seeing if the $y$ values match. 5. Check equation a) $y = 5x$: - For $x = -2$, $y = 5(-2) = -10$ (graph shows 10, no match) 6. Check equation b) $y = -2x + 3$: - For $x = -2$, $y = -2(-2) + 3 = 4 + 3 = 7$ (graph shows 10, no match) 7. Check equation c) $y = 4x + 6$: - For $x = -2$, $y = 4(-2) + 6 = -8 + 6 = -2$ (graph shows 10, no match) 8. None of the equations match the point $(-2, 10)$ exactly, so check other points to find the best fit. 9. Check $x=0$ for each: - a) $y=5(0)=0$ (graph shows 2, no) - b) $y=-2(0)+3=3$ (graph shows 2, close) - c) $y=4(0)+6=6$ (graph shows 2, no) 10. Check $x=1$: - a) $y=5(1)=5$ (graph shows -2, no) - b) $y=-2(1)+3=1$ (graph shows -2, no) - c) $y=4(1)+6=10$ (graph shows -2, no) 11. Check $x=2$: - a) $y=5(2)=10$ (graph shows -6, no) - b) $y=-2(2)+3=-4+3=-1$ (graph shows -6, no) - c) $y=4(2)+6=8+6=14$ (graph shows -6, no) 12. The graph points do not fit any of the given equations exactly, but the pattern of $y$ decreasing as $x$ increases suggests a negative slope. 13. The points roughly follow $y = -4x + 2$ (not given), so none of the equations match Graph A. 14. Therefore, none of the given equations correspond to Graph A based on the points provided. Final answer: No match for Graph A among the given equations.