1. The problem is to graph the linear equation $$y = -\frac{4}{7} x + 6$$. 2. This 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 $$m = -\frac{4}{7}$$ and the y-intercept $$b = 6$$. 4. The y-intercept means the graph crosses the y-axis at the point $$(0, 6)$$. 5. The slope $$-\frac{4}{7}$$ means for every 7 units you move to the right along the x-axis, you move 4 units down along the y-axis. 6. To find the x-intercept, set $$y = 0$$ and solve for $$x$$: $$ 0 = -\frac{4}{7} x + 6 $$ $$ \frac{4}{7} x = 6 $$ $$ x = 6 \times \frac{7}{4} = \frac{42}{4} = 10.5 $$ 7. So the x-intercept is $$(10.5, 0)$$. 8. Plot the points $$(0, 6)$$ and $$(10.5, 0)$$ and draw a straight line through them to graph the equation. Final answer: The graph is a straight line with slope $$-\frac{4}{7}$$ and y-intercept 6, crossing the x-axis at 10.5.