Final answer:
The equation of the line parallel to y=4x+1 and passing through the point (1,1) is y=4x-3. This is found by applying the point-slope form and using the slope of the original line.
Step-by-step explanation:
The student has asked to find the equation of the line parallel to y=4x+1 that also intersects the point (1,1). A line parallel to y=4x+1 will have the same slope, which is 4. Since we know that the point (1,1) lies on the new line, we can use the point-slope form of the equation to find the y-intercept.
The point-slope form equation is y - y1 = m(x - x1), where m is the slope and (x1, y1) is the point that the line crosses. In this case, we have m=4 and our point is (1,1), so substituting these values into our formula gives us:
y - 1 = 4(x - 1)
Simplifying this equation, we get:
y - 1 = 4x - 4
Adding 1 to both sides yields the final equation for the line:
y = 4x - 3