1. The problem asks us to graph a line with a slope of 7 that passes through the point (0, 3). 2. The formula for a line in slope-intercept form is $$y = mx + b$$ where $m$ is the slope and $b$ is the y-intercept. 3. Since the line passes through (0, 3), the y-intercept $b$ is 3. 4. Substitute the slope $m = 7$ and intercept $b = 3$ into the formula: $$y = 7x + 3$$ 5. This means for every increase of 1 in $x$, $y$ increases by 7, starting from 3 when $x=0$. 6. The line equation is now fully determined and can be graphed accordingly.