Final answer:
The equation of line l is y = -5x + 28.
Step-by-step explanation:
To find the equation of a line parallel to line k, we need to find the slope of line k. The equation of line k is 5x + y = 6, which can be rearranged to y = -5x + 6. The coefficient of x, -5, represents the slope. Since line l is parallel to line k, it will have the same slope. Thus, the equation of line l can be written as y = -5x + b, where we need to find the value of b.
We are given that line l passes through the point (5, 3). So, substituting x = 5 and y = 3 in the equation y = -5x + b, we can solve for b. 3 = -5(5) + b => b = 3 + 25 => b = 28. Therefore, the equation of line l is y = -5x + 28.