Start by finding the slope and y-intercept:
slope (y1-y2) / (x1-x2) so:
-2-4 = -6
7-1 = 6
slope = -6/6 or -1
using this information we can find the y-intercept by using the point 1,4 and applying the slope. We know the slope is -1, so if we go backwards from the point 1,4 up one and left one, we hit the y-axis at 0,5. From this we now know our equation:
y = mx + b
m = slope
b = y-intercept
y = -x + 5
To find a perpendicular line, you have to find the reverse reciprocal of the slope, so in this case it is 1. So in this case we could say an equation for a perpendicular line is:
y = x + 5
