Final answer:
To find the equation of a line parallel to y = 4/3x + 7 and passing through (-6,10), we write the equation using the point-slope form. The equation of the parallel line is y = (4/3)x + 18.
Step-by-step explanation:
To find the equation of a line parallel to y = 4/3x + 7, we use the fact that parallel lines have the same slope. The given line has a slope of 4/3, so the parallel line will also have a slope of 4/3. Since the line passes through the point (-6,10), we can use the point-slope form of a linear equation to find the equation of the line:
y - y1 = m(x - x1)
Substituting the values into the equation, we get:
y - 10 = (4/3)(x - (-6))
y - 10 = (4/3)(x + 6)
y - 10 = (4/3)x + 8
y = (4/3)x + 8 + 10
y = (4/3)x + 18
Therefore, the equation of the line parallel to y = 4/3x + 7 and passing through (-6,10) is y = (4/3)x + 18, which corresponds to answer choice d).