Explanation:
"perpendicular" means it creates a right angle (90°) with the original line.
a key element is the slope (the incline) of the line.
it is the factor of x (here 1/4 for the original line) and is defined as the ratio of "y coordinate change / x coordinate change" when going from one point on the line to another.
the given slope of 1/4 means that for every increase in x by 4 units y increases by 1 unit.
now if you want to draw a few random lines, and then draw lines that cross them with a right angle, you will see very quickly the relationship of the slopes of the crossing lines :
for the slope of the perpendicular line x and y of the original slope trade places (the ratio turns "upside-down") and the sign of the slope flips (if the original line goes up, then the perpendicular line goes down and vice versa. so + turns into -, and - into +).
so, our original slope 1/4 turns into -4/1 = -4.
we still have infinite possibilities to draw such a perpendicular line (more up or more down on the coordinate grid).
to finally "nail" one particular line we need to use the given point and solve for the y-intercept.
the general slope-intercept form is
y = ax + b
a is the slope, b is the y-intercept (the y value for x = 0).
so, using the slope (-4) and the point (2, 5) we have
5 = -4×2 + b = -8 + b
13 = b
so, the full equation is
y = -4x + 13