Subjects algebra

Linear Relation

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1. The problem asks to find the values of $y$ in the relation $y = 2(x + 2)$ for given $x$ values and then draw the graph of this relation. 2. The relation is given by the function: $$y = 2(x + 2)$$ 3. We will calculate $y$ for several values of $x$: - For $x = -2$: $$y = 2(-2 + 2) = 2(0) = 0$$ - For $x = 0$: $$y = 2(0 + 2) = 2(2) = 4$$ - For $x = 2$: $$y = 2(2 + 2) = 2(4) = 8$$ - For $x = 3$: $$y = 2(3 + 2) = 2(5) = 10$$ 4. The completed table of values is: | $x$ | $y = 2(x + 2)$ | |-----|----------------| | -2 | 0 | | 0 | 4 | | 2 | 8 | | 3 | 10 | 5. This linear function has a slope of 2 and a y-intercept at $y = 4$ when $x=0$. 6. The graph is a straight line passing through points $(-2,0)$, $(0,4)$, $(2,8)$, and $(3,10)$. Final answer: The relation $y = 2(x + 2)$ evaluated at the given $x$ values produces $y$ values 0, 4, 8, and 10 respectively.