Final answer:
To find the equation for line m given that a and e are points on line l and ae = eb, we need to use the slope-intercept and midpoint formulas. Start by finding the slope of line l and then find the coordinates of point b using the midpoint formula. Substitute those values into the point-slope form of a line to obtain the equation for line m.
Step-by-step explanation:
To find an equation for line m, we need to use the information given in the question. We are told that a and e are points on line l with the equation x - 3y = 18, and a and d are points on line m. We are also given that ae = eb. This means that the distance from a to e is equal to the distance from e to b. Using this information, we can find the equation for line m.
Let's start by finding the slope of line l. The slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept. From the equation x - 3y = 18, we can rewrite it in slope-intercept form: y = (1/3)x - 6. So the slope of line l is 1/3.
Since ae = eb, the point b is the midpoint of line ae. The midpoint formula is (x1 + x2) / 2, (y1 + y2) / 2. Let's say the coordinates of point a are (x1, y1) and the coordinates of point e are (x2, y2). Then the coordinates of point b can be found using the midpoint formula: ((x1 + x2) / 2, (y1 + y2) / 2).
Now we can find the equation for line m. Substitute the coordinates of point a and point b into the point-slope form of a line: y - y1 = m(x - x1). Simplify the equation to get the final form of the equation for line m.