Final answer:
The equation of a line parallel to y = 5x + 1 and passing through the point (4, 5) is y = 5x - 15, as it maintains the same slope of 5 and calculates the y-intercept to meet the designated point.
Step-by-step explanation:
The student is asking how to write the equation of a line that is parallel to the line with the equation y = 5x + 1 and passes through the point (4, 5). To write an equation of a line that is parallel to another, we must have the same slope since parallel lines have identical slopes.
The original line has a slope of 5 (since it's in the form y = mx + b and m is the slope). So, our new line will also have a slope of 5. Now, we just need to find the y-intercept (b) for our new line that goes through the point (4, 5). We do this by plugging the x and y values of the point into the equation y = 5x + b and solving for b:
y = 5x + b
5 = 5(4) + b
5 = 20 + b
b = 5 - 20
b = -15
So, the equation of the line parallel to y = 5x + 1 that passes through the point (4, 5) is y = 5x - 15.