1. **State the problem:** Write the equation of the line in slope-intercept form $y=mx+b$ that passes through the points $(x_1,y_1)$ and $(2,7)$. 2. **Formula for slope:** The slope $m$ of a line through two points $(x_1,y_1)$ and $(x_2,y_2)$ is given by $$m=\frac{y_2 - y_1}{x_2 - x_1}$$ 3. **Calculate the slope:** Substitute $x_2=2$ and $y_2=7$: $$m=\frac{7 - y_1}{2 - x_1}$$ 4. **Use point-slope form:** The equation of the line is $$y - y_1 = m(x - x_1)$$ Substitute $m$: $$y - y_1 = \frac{7 - y_1}{2 - x_1}(x - x_1)$$ 5. **Convert to slope-intercept form:** Distribute the slope: $$y - y_1 = \frac{7 - y_1}{2 - x_1}x - \frac{7 - y_1}{2 - x_1}x_1$$ Add $y_1$ to both sides: $$y = \frac{7 - y_1}{2 - x_1}x - \frac{7 - y_1}{2 - x_1}x_1 + y_1$$ 6. **Final equation:** The slope-intercept form is $$y = \frac{7 - y_1}{2 - x_1}x + \left(y_1 - \frac{7 - y_1}{2 - x_1}x_1\right)$$ This equation represents the line through $(x_1,y_1)$ and $(2,7)$ in slope-intercept form.