1. The problem asks us to draw the line given by the equation $y = 2x + 1$ on the same grid where the line $x + y = 7$ is already drawn. 2. The equation $y = 2x + 1$ is in slope-intercept form $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept. 3. Here, the slope $m = 2$ means the line rises 2 units vertically for every 1 unit 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 draw the line, start at $(0,1)$ on the y-axis. 6. From $(0,1)$, move right 1 unit to $x=1$ and up 2 units to $y=3$, so the point $(1,3)$ is on the line. 7. Repeat this to get more points: at $x=2$, $y=2(2)+1=5$; at $x=3$, $y=7$. 8. Plot these points $(0,1)$, $(1,3)$, $(2,5)$, and $(3,7)$ on the grid and draw a straight line through them. 9. This line will slope upwards and intersect the existing line $x + y = 7$ at some point. Final answer: The line $y = 2x + 1$ passes through points $(0,1)$, $(1,3)$, $(2,5)$, and $(3,7)$ and can be drawn by connecting these points with a straight line on the grid.