1. **State the problem:** We need to graph the line given by the equation $$y = -\frac{2}{3}x + 1$$ on a coordinate grid. 2. **Understand the equation:** This is a linear equation in slope-intercept form $$y = mx + b$$ where $$m$$ is the slope and $$b$$ is the y-intercept. 3. **Identify slope and intercept:** Here, the slope $$m = -\frac{2}{3}$$ and the y-intercept $$b = 1$$. 4. **Plot the y-intercept:** Start by plotting the point where the line crosses the y-axis at $$y=1$$ (point (0,1)). 5. **Use the slope to find another point:** The slope $$-\frac{2}{3}$$ means for every 3 units you move right on the x-axis, move 2 units down on the y-axis (because of the negative sign). 6. **Calculate the next point:** From (0,1), move 3 units right to $$x=3$$ and 2 units down to $$y=1-2= -1$$, so the point is (3, -1). 7. **Draw the line:** Connect the points (0,1) and (3,-1) with a straight line extending across the grid. This line represents the equation $$y = -\frac{2}{3}x + 1$$.