Final answer:
The equation that describes the line passing through (-3, 1) and parallel to y = 4x + 1 is y = 4x + 13.
Step-by-step explanation:
To find the equation of a line that is parallel to the line y = 4x + 1 and passes through the point (-3, 1), we can use the fact that parallel lines have the same slope. The given line has a slope of 4, so the parallel line we are looking for will also have a slope of 4.
Using the point-slope form of a linear equation, where (x1, y1) is the given point and m is the slope, we can substitute (-3, 1) for (x1, y1) and 4 for m to get the equation y - 1 = 4(x - (-3)). Simplifying, we get y - 1 = 4(x + 3). Expanding and rearranging, the equation becomes y = 4x + 13.
Therefore, the equation that describes the line passing through (-3, 1) and parallel to the line y = 4x + 1 is y = 4x + 13.