Final answer:
The equation of the line parallel to y = (3/4)x that passes through the point (2,2) is y = (3/4)x + 1/2, since it has the same slope of 3/4 and the y-intercept is found to be 1/2 when the point (2,2) is plugged into the slope-intercept formula.
Step-by-step explanation:
The student is asking for the equation of a line that is parallel to another line and passes through a specific point. A line that is parallel to another will have the same slope, so we begin by identifying the slope of the given line y = (3/4)x, which is 3/4. For our new line to be parallel, it must also have a slope of 3/4.
The general form of a line's equation is y = mx + b, where m is the slope and b is the y-intercept. Since the new line must pass through the point (2,2) and we already know the slope is 3/4, we can substitute these values into the slope-intercept form to find b. So we have 2 = (3/4)*2 + b, which simplifies to 2 = 3/2 + b. Subtracting 3/2 from both sides gives us b = 1/2.
Therefore, the equation of the line that passes through the point (2,2) and is parallel to the line y = (3/4)x is y = (3/4)x + 1/2.