Linear Function 41Ab13

1. **State the problem:** We are given the function $$y = -3x$$ and need to fill in the table of values for $$x = -3, -2, -1, 0, 1, 2, 3$$ and then use these values to graph the function. 2. **Formula used:** The function is linear and given by $$y = -3x$$. This means for each value of $$x$$, multiply by $$-3$$ to find $$y$$. 3. **Calculate each value:** - For $$x = -3$$: $$y = -3 \times (-3) = 9$$ - For $$x = -2$$: $$y = -3 \times (-2) = 6$$ - For $$x = -1$$: $$y = -3 \times (-1) = 3$$ - For $$x = 0$$: $$y = -3 \times 0 = 0$$ - For $$x = 1$$: $$y = -3 \times 1 = -3$$ - For $$x = 2$$: $$y = -3 \times 2 = -6$$ - For $$x = 3$$: $$y = -3 \times 3 = -9$$ 4. **Completed table:** | x | y = -3x | |----|---------| | -3 | 9 | | -2 | 6 | | -1 | 3 | | 0 | 0 | | 1 | -3 | | 2 | -6 | | 3 | -9 | 5. **Graph shape explanation:** The graph is a straight line passing through the origin $$(0,0)$$. Since the slope is $$-3$$, the line decreases steeply from top-left to bottom-right. 6. **Summary:** We found the $$y$$ values by multiplying each $$x$$ by $$-3$$ and confirmed the graph is a straight line with negative slope passing through the origin.