What is the equation of a line that passes through the point (10, 5) and is perpendicular to the line whose equation is y=54x−2y=54x−2 ?

We need to get the reciprocal of the slope to become reciprocal. To get the reciprocal of m, or slope, switch the numerator and denominator with each other and flip the sign.

54/1 ⇒ 1/54 ⇒ -1/54

y = -1/54x + b

Now, input the coordinate point and solve for b.

5 = -1/54(10) + b
Simplify.
5 = -0.185185185 + b
Add 0.185185185 to both sides.
5.18518519, or 140/27 = b

y = -1/54x + 140/27