Identify the slope of the given line
If we rewrite the equation given, we can easily identify the slope
x - 5y = 6
- 5y = - x + 6
y = ¹/₅ x - ⁶/₅
∴ the slope of x - 5y = 6 is ¹/₅
Find the slope of the perpendicular line
When two lines are perpendicular, the product of their slopes is -1. This means that the slopes are negative-reciprocals of each other.
⇒ since the slope of this line = ¹/₅
then the slope of the perpendicular line (m) = - 5
Determine the equation of perpendicular line
We can now use the point-slope form (y - y₁) = m(x - x₁)) to write the equation for this line:
⇒ y - (-10) = - 5 (x - 2)
We can also write the equation in the slope-intercept form by making y the subject of the equation and expanding the bracket to simplify:
since y + 10 = - 5 (x - 2)
To test my answer, I have included a Desmos Graph that I graphed using the information provided in the question and my answer.
