Final answer:
To find the equation of the line that cuts off equal intercepts on the coordinate axes and passes through (2, 5), determine the value of the slope, m, and the y-intercept, b. Use the coordinates of the given point to write two equations: 2d = 5 and d + 0 = 2d. Solve these equations to find the equation of the line: y = x - 5/2.
Step-by-step explanation:
To find the equation of the line that cuts off equal intercepts on the coordinate axes and passes through (2, 5), we need to determine the value of the slope, m, and the y-intercept, b. Since the line cuts off equal intercepts, the x-intercept and y-intercept will be the same distance from the origin. Let's call this distance 'd'.
Since the x-intercept is (d, 0) and the y-intercept is (0, d), we can use the coordinates of the given point (2, 5) to write two equations: 2d = 5 and d + 0 = 2d.
Solving these equations gives us d = 5/2. Therefore, the equation of the line is y = x - 5/2.