Final answer:
The equation for a line parallel to y = 4x and passing through the point (-1,3) is y = 4x + 7, since both lines have the same slope of 4, but different y-intercepts.
Step-by-step explanation:
The equation for a line parallel to y = 4x and passing through the point (-1,3) will have the same slope as the given line since parallel lines have identical slopes.
The given line has a slope of 4, so our new line will also have a slope of 4.
Using the point-slope form of a line, which is y - y₁ = m(x - x₁), where (x₁, y₁) is a point on the line and m is the slope, we can plug in our values to obtain the equation.
The equation becomes y - 3 = 4(x + 1).
Simplifying this, we get y - 3 = 4x + 4 and then adding 3 to both sides gives us the final equation y = 4x + 7.