Final answer:
The equation of the line parallel to y = x + 8 and passing through (-12, 4) is y - 4 = x + 12, using the point-slope form of a line equation and the fact that parallel lines have the same slope.
Step-by-step explanation:
To find the equation of a line parallel to y = x + 8 that goes through the point (-12,4), we first need to identify the slope of the given line. The slope-intercept form of a line is y = mx + b, where m is the slope, and b is the y-intercept. For the line y = x + 8, the slope m is 1 because the coefficient of x is 1.
Since parallel lines have the same slope, the new line will also have a slope of 1. Now, we apply the point-slope form of the equation of a line, which is y - y1 = m(x - x1), where (x1, y1) is a point on the line and m is the slope. Substituting the given point (-12, 4) and the slope 1, we get the equation: y - 4 = 1(x - (-12))
Simplifying, our final equation in point-slope form is: y - 4 = x + 12.