Final answer:
The equation for the line parallel to y = 3/4x + 4 that passes through the point (2,2) is y = 3/4x + 1/2.
Step-by-step explanation:
To find the equation for a line that is parallel to another given line, we need to determine the slope of the given line first. The slope of the given line y = 3/4x + 4 is 3/4. Since the parallel line has the same slope, the equation for the parallel line is y = 3/4x + b, where b is the y-intercept. To find the value of b, we can substitute the x and y coordinates of the given point (2,2) into the equation and solve for b:
2 = (3/4)(2) + b
2 = 3/2 + b
b = 2 - 3/2
b = 1/2
Therefore, the equation for the line that passes through the point (2,2) and is parallel to the line y = 3/4x + 4 is y = 3/4x + 1/2.