1. The problem asks us to identify which graph corresponds to the function rule $y = -4 + 3x$. 2. The function is a linear equation in slope-intercept form $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept. 3. Here, the slope $m = 3$ and the y-intercept $b = -4$. This means the line crosses the y-axis at $(0, -4)$ and rises 3 units vertically for every 1 unit it moves horizontally. 4. Let's check the points given for each graph to see which satisfy $y = -4 + 3x$. - Left graph points: $(-2, -10)$, $(0, -4)$, $(3, 5)$ - For $x = -2$, $y = -4 + 3(-2) = -4 - 6 = -10$ (matches) - For $x = 0$, $y = -4 + 0 = -4$ (matches) - For $x = 3$, $y = -4 + 9 = 5$ (matches) - Center graph points: $(-3, -13)$, $(-1, -7)$, $(2, 2)$ - For $x = -3$, $y = -4 + 3(-3) = -4 - 9 = -13$ (matches) - For $x = -1$, $y = -4 + 3(-1) = -4 - 3 = -7$ (matches) - For $x = 2$, $y = -4 + 6 = 2$ (matches) - Right graph points: $(-3, 5)$, $(-1, -1)$, $(2, -10)$ - For $x = -3$, $y = -4 + 3(-3) = -13$ (does not match 5) 5. Both the left and center graphs have points that satisfy the function, but the position hint says "center". 6. Therefore, the center graph is the correct graph of the function $y = -4 + 3x$. Final answer: The center graph represents the function $y = -4 + 3x$.