Final answer:
The slope of a line perpendicular to the line with equation 6x + 15y = 225 is 5/2.
Step-by-step explanation:
The equation of the given line is 6x + 15y = 225. To find the slope of this line, we need to rearrange the equation in the form y = mx + b, where m is the slope. Let's rearrange the equation:
6x + 15y = 225
15y = -6x + 225
y = (-6/15)x + 15
Now we can see that the slope of the given line is -6/15.
To find the slope of a line perpendicular to the given line, we need to take the negative reciprocal of the slope of the given line. The negative reciprocal of -6/15 is 15/6, which can be simplified to 5/2. So, the slope of a line perpendicular to the given line is 5/2.