1. **State the problem:** We are given the linear equation $$-3x + y = 2$$ and a table of values for $x$: -1, 0, 1. We need to find the corresponding $y$ values and understand the line it represents. 2. **Formula and rules:** The equation is in standard form. To find $y$ for each $x$, solve for $y$: $$y = 3x + 2$$ This is because adding $3x$ to both sides gives $y = 3x + 2$. 3. **Calculate $y$ values:** - For $x = -1$: $$y = 3(-1) + 2 = -3 + 2 = -1$$ - For $x = 0$: $$y = 3(0) + 2 = 0 + 2 = 2$$ - For $x = 1$: $$y = 3(1) + 2 = 3 + 2 = 5$$ 4. **Summary:** The points on the line are $(-1, -1)$, $(0, 2)$, and $(1, 5)$. The line has slope 3 and y-intercept 2. 5. **Interpretation:** This means for every increase of 1 in $x$, $y$ increases by 3. The line crosses the y-axis at 2. **Final answer:** The equation in slope-intercept form is $$y = 3x + 2$$ and the points are $(-1, -1)$, $(0, 2)$, and $(1, 5)$.