Line Table Graph 580Ad6

1. **State the problem:** We are given the linear equation $$y = -2x + 5$$ and asked to complete a table of values for $x = -1, 0, 3$ and then graph the equation. 2. **Formula and rules:** The equation is in slope-intercept form $$y = mx + b$$ where $m$ is the slope and $b$ is the y-intercept. 3. **Calculate $y$ for each $x$ value:** - For $x = -1$: $$y = -2(-1) + 5 = 2 + 5 = 7$$ - For $x = 0$: $$y = -2(0) + 5 = 0 + 5 = 5$$ - For $x = 3$: $$y = -2(3) + 5 = -6 + 5 = -1$$ 4. **Complete the table:** | $x$ | $y$ | |-----|-----| | -1 | 7 | | 0 | 5 | | 3 | -1 | 5. **Graph the equation:** - The graph is a straight line passing through the points $(-1,7)$, $(0,5)$, and $(3,-1)$. - The slope $m = -2$ means the line goes down 2 units for every 1 unit it moves to the right. - The y-intercept $b = 5$ is where the line crosses the y-axis. **Final answer:** The completed table is: | $x$ | $y$ | |-----|-----| | -1 | 7 | | 0 | 5 | | 3 | -1 |