1. The problem is to sketch the graph of the line given by the equation $y = -\frac{3}{2}x + 1$. 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 $m = -\frac{3}{2}$ means the line falls 3 units vertically for every 2 units it moves horizontally to the right. 4. The y-intercept $b = 1$ means the line crosses the y-axis at the point $(0,1)$. 5. To find the x-intercept, set $y=0$ and solve for $x$: $$0 = -\frac{3}{2}x + 1$$ $$\frac{3}{2}x = 1$$ $$x = \frac{1}{\frac{3}{2}} = \frac{1}{1} \times \frac{2}{3} = \frac{2}{3}$$ 6. So the x-intercept is at $\left(\frac{2}{3}, 0\right)$. 7. Plot the points $(0,1)$ and $\left(\frac{2}{3}, 0\right)$ on the coordinate plane and draw a straight line through them. This line slopes downward from left to right because the slope is negative. Final answer: The graph is a straight line crossing the y-axis at 1 and the x-axis at $\frac{2}{3}$ with slope $-\frac{3}{2}$.