The slope of our line y = x/4 + 5 is m = 1/4
Since we're coming up with the equation of a line that is perpendicular, the slope of our perpendicular line is the opposite reciprocal of 1/4, or m = - 4/1 or m = 4
Now, we need to find out the y-intercept of our perpendicular line. To do that we plug in (2, 7) into x and y as well as - 4 into m in the following equation:
y = mx + b
7 = (- 4)(2) + b
7 = - 8 + b
15 = b
Thus, with m = - 4 and b = 15, the equation of our perpendicular line is:
y = - 4x + 15
WARNING: Possibly wrong~ Hannah