1. The problem asks to analyze and graph the line given by the equation $y = 3x - 6$. 2. First, identify the slope and the y-intercept. - The equation is in slope-intercept form $y = mx + b$ where $m = 3$ and $b = -6$. - So, the slope is 3 and the y-intercept is at $(0, -6)$. 3. To graph the line, plot the y-intercept at $(0, -6)$ on the coordinate plane. 4. Use the slope to find another point. Since the slope is 3, rise over run is $3/1$: - From $(0, -6)$, move up 3 units and right 1 unit to $(1, -3)$. 5. Plot the point $(1, -3)$ and draw a straight line through the points. 6. Optional: Find the x-intercept by setting $y=0$: $$0 = 3x - 6$$ $$3x = 6$$ $$x = 2$$ So the x-intercept is at $(2, 0)$. 7. Summary: - Slope: 3 - y-intercept: $(0, -6)$ - x-intercept: $(2, 0)$ - The line passes through points $(0, -6)$ and $(2, 0)$. This matches the points for graphing. Final answer: The equation $y = 3x - 6$ defines a line with slope 3 and intercepts $(0, -6)$ and $(2, 0)$.