1. The problem asks for the equation of the line passing through points (0,7) and (7,0) in slope-intercept form $y=mx+b$. 2. The slope-intercept form is $y=mx+b$, where $m$ is the slope and $b$ is the y-intercept. 3. Calculate the slope $m$ using the formula $$m=\frac{y_2 - y_1}{x_2 - x_1}$$ where $(x_1,y_1)=(0,7)$ and $(x_2,y_2)=(7,0)$. 4. Substitute values: $$m=\frac{0 - 7}{7 - 0}=\frac{-7}{7}=-1$$ 5. The y-intercept $b$ is the y-coordinate when $x=0$, which is $7$. 6. Substitute $m$ and $b$ into the slope-intercept form: $$y = -1x + 7$$ or simply $$y = -x + 7$$ 7. This is the equation of the line in slope-intercept form. Final answer: $$y = -x + 7$$