Final answer:
The equation that describes a line parallel to y = 4x + 1, passing through (-3, 1), is y = 4x + 13. The slope must be the same for lines to be parallel, and by substituting the point into the slope-intercept formula, we find the y-intercept to be 13.
Step-by-step explanation:
The question asks which equation describes a line that is parallel to the line given by y = 4x + 1 and passes through the point (-3, 1). To be parallel, a line must have the same slope as the line to which it is parallel. The given line has a slope of 4, so our parallel line must also have a slope of 4. The equation of a line in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept. Using the point (-3,1), we substitute the coordinates into the slope-intercept equation and solve for b:
- 1 = 4(-3) + b
- 1 = -12 + b
- b = 13
Therefore, the equation of the line is y = 4x + 13, which matches option B.