<h3>Answer: </h3><h3>y + 10 = - 5 (x - 2) [point-slope form] OR</h3><h3>y = - 5 x [slope-intercept form]</h3><h2 /><h3>Step-by-step explanation:</h3>

<u>**Identify the slope of the given line**</u>

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

<u>**Find the slope of the perpendicular line**</u>

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**

<u>**Determine the equation of perpendicular line**</u>

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)

<h3> ∴ y + 10 = - 5 (x - 2)</h3><h3 />

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)

<h3> y = - 5 x</h3><h3 /><h3>∴ the slope-intercept equation of the perpendicular line is y + 10 = - 5 (x - 2) OR y = - 5 x.
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<em>To test my answer, I have included a Desmos Graph that I graphed using the information provided in the question and my answer.</em>