Final answer:
The equation of the line that is parallel to y = 2/3x - 7 and passes through the point (5, 7) is y = 2/3x + 11/3.
Step-by-step explanation:
The equation representing the line that passes through the point (5, 7) and is parallel to the graph of y = 2/3x - 7 will have the same slope as the given line.
Since parallel lines have identical slopes, we maintain the slope of 2/3. To find the new line's equation, we use the point-slope form: y - y1 = m(x - x1), where (x1, y1) is the point the line passes through and m is the slope.
Plugging in the given point and slope, we have:
y - 7 = 2/3(x - 5).
This simplifies to:
y = 2/3x + 2/3(5) - 7,
y = 2/3x -10/3 + 21/3,
y = 2/3x + 11/3.
Therefore, the equation of the line parallel to y = 2/3x - 7 and passing through the point (5, 7) is y = 2/3x + 11/3.