The equation y= -4x + 1 is in the "slope-intercept" form of y=mx+b, where m is the slope (rise over run), and b is the y-intercept (where the line will cross the vertical y-axis).
You need graph paper for an accurate graph (but it's possible to do it on notebook paper).
It's best to start at the y-intercept and plot your first point there. Put a dot on the y-axis 1 unit up from the origin.
I like to rewrite the slope as a fraction, to better visualize the "rise over run" so -4 becomes -4/1. This means I rise negative 4 (fall 4) and run to the right 1.
So, starting at the dot you made at the y-intercept, count down 4 units, then right 1 unit, and draw your second dot. You can repeat the process starting there for more points: count down 4, then right 1.
Lastly, you can go back to the y-intercept and count in the opposite direction, since your slope is also equal to positive 4 over negative 1. You can then count UP 4 units, and LEFT 1 unit.