1. The problem is to graph the line given by the equation $y = 4x + 1$ using the slope and y-intercept. 2. The slope-intercept form of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept. 3. From the equation $y = 4x + 1$, the slope $m = 4$ and the y-intercept $b = 1$. 4. The y-intercept is the point where the line crosses the y-axis, so plot the point $(0,1)$. 5. The slope $4$ means that for every 1 unit increase in $x$, $y$ increases by 4 units. 6. Starting from $(0,1)$, move 1 unit right to $x=1$ and 4 units up to $y=5$, plot the point $(1,5)$. 7. Connect these points with a straight line extending in both directions. 8. This line represents all points $(x,y)$ satisfying $y = 4x + 1$. Final answer: The line passes through points $(0,1)$ and $(1,5)$ with slope 4.