1. **State the problem:** We need to graph the line given by the equation $$y = -\frac{4}{3}x + 6$$ and understand its key features. 2. **Identify the slope and y-intercept:** The equation is in slope-intercept form $$y = mx + b$$ where $$m$$ is the slope and $$b$$ is the y-intercept. Here, $$m = -\frac{4}{3}$$ and $$b = 6$$. 3. **Plot the y-intercept:** The line crosses the y-axis at $$y = 6$$, so one point is at $$(0, 6)$$. 4. **Use the slope to find another point:** The slope $$-\frac{4}{3}$$ means for every increase of 3 units in $$x$$, $$y$$ decreases by 4 units. Starting from $$(0, 6)$$, move right 3 units to $$x = 3$$ and down 4 units to $$y = 6 - 4 = 2$$, giving the point $$(3, 2)$$. 5. **Plot these points and draw the line:** Connect the points $$(0, 6)$$ and $$(3, 2)$$ with a straight line extending in both directions. 6. **Check the points given:** The points $$(-1.5, 8)$$ and $$(1, 2.67)$$ lie on the line, consistent with the slope and intercept. **Final answer:** The line $$y = -\frac{4}{3}x + 6$$ passes through $$(0, 6)$$ and $$(3, 2)$$ with slope $$-\frac{4}{3}$$, descending from left to right.