To determine the equation of the line perpendicular to this line, we can first put the equation of the line in slope-intercept form by moving the 5x to the other side:
5x - 5x + 4y = 10 - 5x
⇒ 4y = -5x + 10
Next, we divide all sides by 4 to isolate y:
y = -5/4x + 5/2
Now, we must implement the opposite reciprocal principle to obtain the slope of the perpendicular line:
-5/4 ⇒ 4/5
Then, we plug this value into the given point (5,12):
12 = 4/5(5) + b
⇒ 12 = 4 + b
⇒ b = 8
Therefore, the equation of the line perpendicular to the line 5x + 4y = 10 is y = 4/5x + 8.
