Answer: y = - ²/₅ x - ²/₅ OR y - 2 = - ²/₅ (x + 6)
Step-by-step 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 = ⁵/₂
then the slope of the perpendicular line (m) = - ²/₅
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 = - ²/₅ (x - (-6))
∴ y - 2 = - ²/₅ (x + 6)
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 - 2 = - ²/₅ (x + 6)
y = - ²/₅ x - ²/₅ (slope-intercept form)
To test my answer, I have included a Desmos Graph that I graphed using the information provided in the question and my answer.
