Graph Points D76D4B

1. **State the problem:** We need to check which of the points $$(0,2), (0,3), (3,4), (3,9)$$ lie on the graph of the linear equation $$y = 2x + 3$$. 2. **Formula used:** The equation of the line is $$y = 2x + 3$$. A point $$(x,y)$$ lies on the graph if substituting $$x$$ into the equation gives the corresponding $$y$$. 3. **Check each point:** - For $$(0,2)$$: Substitute $$x=0$$ into $$y=2x+3$$: $$y = 2(0) + 3 = 3$$ The point has $$y=2$$ but the equation gives $$3$$, so $$(0,2)$$ is **not** on the graph. - For $$(0,3)$$: Substitute $$x=0$$: $$y = 2(0) + 3 = 3$$ The point has $$y=3$$ which matches, so $$(0,3)$$ **is** on the graph. - For $$(3,4)$$: Substitute $$x=3$$: $$y = 2(3) + 3 = 6 + 3 = 9$$ The point has $$y=4$$ but the equation gives $$9$$, so $$(3,4)$$ is **not** on the graph. - For $$(3,9)$$: Substitute $$x=3$$: $$y = 2(3) + 3 = 9$$ The point has $$y=9$$ which matches, so $$(3,9)$$ **is** on the graph. 4. **Final answer:** The points on the graph are $$(0,3)$$ and $$(3,9)$$.