Final answer:
The equation of the perpendicular line is 3x + 2y = 0.
Step-by-step explanation:
To find the equation of the other line that is perpendicular to the given line, we need to determine its slope. Since the given line has a slope of 2/3, we know that the slope of the perpendicular line will be the negative reciprocal of 2/3. The negative reciprocal of 2/3 is -3/2. Therefore, the equation of the other line can be written in the form y = mx + b as y = (-3/2)x + b.
Now, we can use the fact that the lines intersect on the x-axis to find the y-intercept (b). Since the point of intersection is on the x-axis, the y-coordinate of the point is 0. Plugging in these values into the equation, we get 0 = (-3/2)(0) + b, simplifying to 0 = 0 + b. Therefore, b = 0. So, the equation of the other line is y = (-3/2)x.