Final answer:
To find the equation of the line that is parallel to y = (1/5)x - 5 and passes through the point (0,6), we can determine the slope of the given line and use it to construct the equation of the new line.
Step-by-step explanation:
To find the equation of the line that is parallel to y = (1/5)x - 5 and passes through the point (0,6), we need to determine the slope of the given line and use it to construct the equation of the new line. The slope of the given line is 1/5. Since the new line is parallel, it will also have a slope of 1/5. Using the slope-intercept form of a linear equation, y = mx + b, where m is the slope and b is the y-intercept, we can substitute the values of m = 1/5 and (0,6) into the equation to find the y-intercept.
Substituting the point (0,6) and slope m = 1/5 into the equation, we get 6 = (1/5)(0) + b. Solving for b, we find that b = 6. Therefore, the equation of the line parallel to y = (1/5)x - 5 and passing through the point (0,6) is y = (1/5)x + 6.