Final answer:
To find the coordinates of the point where the line L crosses the x-axis, substitute x=0 into the equation y=2x+8. The coordinates of point A are (0, 8). The equation of line M, which is perpendicular to line L and passes through point A, is y=-1/2x+8.
Step-by-step explanation:
To find the coordinates of the point where the line L crosses the x-axis, we need to find the value of y when x = 0. We substitute x = 0 into the equation y = 2x + 8, which gives us y = 2(0) + 8 = 8. Therefore, the point A has coordinates (0, 8).
The line M is perpendicular to line L, which means its slope is the opposite reciprocal of the slope of line L. The slope of line L is 2, so the slope of line M is -1/2. Since line M passes through point A and has slope -1/2, its equation can be written in the form y = mx + b, where m = -1/2 and we need to find the value of b. We substitute the coordinates of point A (0, 8) into the equation and solve for b:
8 = -1/2(0) + b
8 = b
Therefore, the equation of line M is y = -1/2x + 8.