Final answer:
To write the equation of a line parallel to Line A, use the same slope and find the y-intercept. For a line perpendicular to Line A, use the negative reciprocal of the slope and find the y-intercept.
Step-by-step explanation:
To write the equation of a line parallel to Line A, we need to find the slope of Line A. The given equation y = 1/4x + 5 is in slope-intercept form, where the coefficient of x represents the slope. So, the slope of Line A is 1/4. Since parallel lines have the same slope, the equation of a line parallel to Line A would also have a slope of 1/4. The equation can be written as y = 1/4x + b, where b is the y-intercept to be determined.
To find the equation of a line perpendicular to Line A, we need to find the negative reciprocal of the slope of Line A. The negative reciprocal of 1/4 is -4/1 or -4. So, the slope of the perpendicular line would be -4. The equation can be written as y = -4x + b, where b is the y-intercept to be determined.