Answer: y + 2 = - ¹/₇ (x - 3)
Explanation:
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.
⇒ if the slope of this line = 7
then the slope of the perpendicular line (m) = - ¹/₇
Determine the equation
We can now use the point-slope form (y - y₁) = m(x - x₁)) to write the equation for this line:
⇒ y - (-2) = - ¹/₇ (x - 3)
∴ y + 2 = - ¹/₇ (x - 3)
To test my answer, I have included a Desmos Graph that I graphed using the information provided in the question and my answer.