1. **State the problem:** We are given three linear equations: $$y = 5x$$ $$y = -2x + 3$$ $$y = 4x + 6$$ and a set of points plotted on a coordinate plane: $(-2, 6), (-1, 4), (0, 3), (1, 2), (2, 0)$. We want to understand these lines and how they relate to the points. 2. **Recall the formula for a line:** The general form is $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept. 3. **Analyze each line:** - For $y = 5x$, slope $m=5$, intercept $b=0$. - For $y = -2x + 3$, slope $m=-2$, intercept $b=3$. - For $y = 4x + 6$, slope $m=4$, intercept $b=6$. 4. **Check which line fits the points:** - Test point $(-2,6)$ in each equation: - $y=5x$: $5(-2) = -10 eq 6$ - $y=-2x+3$: $-2(-2)+3=4+3=7 eq 6$ - $y=4x+6$: $4(-2)+6=-8+6=-2 eq 6$ - Test point $(-1,4)$: - $5(-1)=-5 eq 4$ - $-2(-1)+3=2+3=5 eq 4$ - $4(-1)+6=-4+6=2 eq 4$ - Test point $(0,3)$: - $5(0)=0 eq 3$ - $-2(0)+3=3 = 3$ (matches) - $4(0)+6=6 eq 3$ - Test point $(1,2)$: - $5(1)=5 eq 2$ - $-2(1)+3=-2+3=1 eq 2$ - $4(1)+6=4+6=10 eq 2$ - Test point $(2,0)$: - $5(2)=10 eq 0$ - $-2(2)+3=-4+3=-1 eq 0$ - $4(2)+6=8+6=14 eq 0$ 5. **Conclusion:** None of the given lines perfectly fit all the points. However, the point $(0,3)$ lies on the line $y = -2x + 3$. 6. **Interpretation:** The points plotted do not lie on any of the three given lines exactly. The line $y = -2x + 3$ passes through $(0,3)$, but the other points do not satisfy any of the equations. **Final answer:** The points do not lie on any of the lines $y=5x$, $y=-2x+3$, or $y=4x+6$ except for $(0,3)$ on $y=-2x+3$.