Final answer:
The equation of a line parallel to y = 2x + 7 and passing through (-4, 7) is y = 2x + 15. Since parallel lines have the same slope, we use the given point to solve for the y-intercept, leading us to option B.
Step-by-step explanation:
To write the equation of a line in slope-intercept form that is parallel to the line y = 2x + 7 and goes through the point (-4, 7), you must use the slope of the given line and the coordinates of the given point. The slope-intercept form of a line is given by y = mx + b, where m is the slope and b is the y-intercept. Since the lines are parallel, they must have the same slope. Therefore, the slope m will also be 2, as it is in the given equation y = 2x + 7. To find the y-intercept b, we can plug in the coordinates (-4, 7) into the slope-intercept form:
7 = 2(-4) + b
7 = -8 + b
7 + 8 = b
b = 15
Therefore, the equation of the line is y = 2x + 15, which corresponds to option B.