1. **State the problem:** We are given the linear function $y = 2x + 2$ and a table of values for $x$ and $y$. We want to understand how the function works and verify the points. 2. **Formula and rules:** The function is in slope-intercept form $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept. 3. **Identify slope and intercept:** Here, $m = 2$ means for every increase of 1 in $x$, $y$ increases by 2. The y-intercept $b = 2$ means the graph crosses the y-axis at $(0, 2)$. 4. **Verify points:** Substitute each $x$ value into $y = 2x + 2$: - For $x = -3$: $y = 2(-3) + 2 = -6 + 2 = -4$ - For $x = -2$: $y = 2(-2) + 2 = -4 + 2 = -2$ - For $x = -1$: $y = 2(-1) + 2 = -2 + 2 = 0$ - For $x = 0$: $y = 2(0) + 2 = 0 + 2 = 2$ - For $x = 1$: $y = 2(1) + 2 = 2 + 2 = 4$ - For $x = 2$: $y = 2(2) + 2 = 4 + 2 = 6$ - For $x = 3$: $y = 2(3) + 2 = 6 + 2 = 8$ All points match the table. 5. **Interpretation:** The graph is a straight line with slope 2, rising upward from left to right, crossing the y-axis at 2. **Final answer:** The function $y = 2x + 2$ correctly models the given points and has slope 2 and y-intercept 2.