Write an equation of the line that is perpendicular to y = −4x + 8 and passes through the point (5, 1)

Hello, 

To start, we have to identify the slope of the perpendicular line. Perpendicular lines have opposite reciprocal slopes. Therefore, the slope of our new line will be 1/4. 

Now, just substitute in the given point with our new slope and we can solve for B.

y = (1/4)x + b
1 = (1/4)5 + b
1 = 5/4 + b
-1/4 = b

Now that we have the slope and the y-intercept, we can put together our equation.

It is: y = (1/4)x - 1/4

Good luck,
MrEQ