1. The problem is to graph the line given by the equation $y = -2x + 1$. 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. From the equation, the slope $m = -2$ and the y-intercept $b = 1$. 4. To graph the line, start at the y-intercept point $(0,1)$ on the coordinate plane. 5. Use the slope to find another point. Since the slope is $-2$, it means for every 1 unit increase in $x$, $y$ decreases by 2 units. 6. From $(0,1)$, move right 1 unit to $x=1$, then down 2 units to $y = 1 - 2 = -1$. This gives the point $(1,-1)$. 7. Plot the points $(0,1)$ and $(1,-1)$ and draw a straight line through them extending in both directions. 8. This line represents all solutions to the equation $y = -2x + 1$. Final answer: The graph is a straight line crossing the y-axis at 1 and sloping downward with slope $-2$.