1. **State the problem:** We need to find the equation of a line perpendicular to line AB that passes through the point (7, 6). 2. **Find the slope of line AB:** The line AB passes through points A(0, 1) and B(-2, 5). The slope formula is $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ Calculate: $$m_{AB} = \frac{5 - 1}{-2 - 0} = \frac{4}{-2} = -2$$ 3. **Find the slope of the perpendicular line:** The slope of a line perpendicular to another is the negative reciprocal of the original slope. So, $$m_{perp} = -\frac{1}{m_{AB}} = -\frac{1}{-2} = \frac{1}{2}$$ 4. **Use point-slope form to find the equation:** The point-slope form is $$y - y_1 = m(x - x_1)$$ Substitute $m = \frac{1}{2}$ and point $(7, 6)$: $$y - 6 = \frac{1}{2}(x - 7)$$ 5. **Simplify to slope-intercept form:** $$y - 6 = \frac{1}{2}x - \frac{7}{2}$$ Add 6 to both sides: $$y = \frac{1}{2}x - \frac{7}{2} + 6$$ Convert 6 to halves: $$6 = \frac{12}{2}$$ So, $$y = \frac{1}{2}x + \frac{5}{2}$$ 6. **Final answer:** $$\boxed{y = 0.5x + 2.5}$$ This matches the first option given.