Final answer:
The equation of the line that passes through the point (-1, 8) and is parallel to the line y = 9 + 3x is y = 3x + 11.
Step-by-step explanation:
To find the equation of the line that passes through the point (-1, 8) and is parallel to the line y = 9 + 3x, we should note that parallel lines have the same slope. In this case, since the slope (m) is 3, our unknown line must also have a slope of 3. Using the point-slope form of a line which is y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope, we can substitute the values to find the equation of our unknown line.
Plugging in slope 3 and the coordinates of the point (-1, 8) into the point-slope form, we get:
y - 8 = 3(x - (-1))
y - 8 = 3(x + 1)
y - 8 = 3x + 3
To write it in slope-intercept form, we add 8 to both sides, resulting in:
y = 3x + 11
This is the equation of the line passing through the point (-1, 8) and parallel to the given line.