Final answer:
The equation of the line, in slope-intercept form, that contains the point (-12, 5) and is parallel to the line y = 3x + 6 is y = 3x + 31.
Step-by-step explanation:
To find the equation of the line that is parallel to y = 3x + 6 and passes through the point (-12, 5), we need to use the fact that parallel lines have the same slope. The given line has a slope of 3, so the parallel line will also have a slope of 3. We can use the point-slope form of a linear equation to find the equation of the parallel line:
y - y1 = m(x - x1)
where (x1, y1) is the given point and m is the slope. Substituting (-12, 5) for (x1, y1) and 3 for m, we get:
y - 5 = 3(x + 12)
Now, we can simplify this equation to slope-intercept form:
y = 3x + 36 - 5
y = 3x + 31