Final answer:
The relationship between the line with the equation 3y = 15x + 1 and the curve y = x⁵ + 3 is 'Neither' parallel nor perpendicular, as one represents a linear equation with a constant slope and the other represents a polynomial curve with a variable slope.
Step-by-step explanation:
To determine the relationship between the lines 3y = 15x + 1 and y = x⁵ + 3, we need to look at the slopes of these lines. For the first equation, we can simplify it to find the slope by dividing all terms by 3, yielding y = 5x + 1/3. The slope of this line, represented by 'm', is 5.
The second equation is not linear; it's a polynomial of degree 5, represented as y = x⁵ + 3. Since it's a higher-degree polynomial, its graph will not be a straight line but rather a curve that changes slopes at different intervals.
When comparing these two slopes, it becomes apparent that they are not related in a way that would make them parallel or perpendicular. The first line has a constant slope of 5, whereas the slope of the second line is not constant and cannot be compared linearly to the first line. Therefore, based on their slopes, we conclude the relationship between them is c) Neither parallel nor perpendicular because one is a straight line and the other is a curve.