1. **Stating the problem:** Find the equation of the line passing through points A(4,9) and B(5,7), and find the x-intercept of this line. 2. **Formula for the equation of a line through two points:** The slope $m$ is given by $$m=\frac{y_2 - y_1}{x_2 - x_1}$$ The equation of the line is $$y - y_1 = m(x - x_1)$$ 3. **Calculate the slope $m$:** $$m=\frac{7 - 9}{5 - 4} = \frac{-2}{1} = -2$$ 4. **Write the equation using point A(4,9):** $$y - 9 = -2(x - 4)$$ Simplify: $$y - 9 = -2x + 8$$ $$y = -2x + 17$$ 5. **Find the x-intercept:** At the x-intercept, $y=0$, so $$0 = -2x + 17$$ $$2x = 17$$ $$x = \frac{17}{2} = 8.5$$ **Final answers:** - Equation of line AB: $$y = -2x + 17$$ - x-intercept of line AB: $$x = 8.5$$