Answer: y = ¹/₆ x + 22.
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 one of the lines = - 6
then the slope of the perpendicular line (m) = ¹/₆
Determine the equation
We can now use the point-slope form (y - y₁) = m(x - x₁)) to write the equation for this line:
⇒ y - 20 = ¹/₆ (x - (-12))
∴ y - 20 = ¹/₆ (x + 12)
We can also write the equation in the slope-intercept form (y=mx+c) like the equation in the question by making y the subject of the equation and expanding the bracket to simplify:
since y - 20 = ¹/₆ (x + 12)
y - 20 = ¹/₆x + 2
y = ¹/₆x + 22
∴ the slope-intercept equation of the perpendicular line is y = ¹/₆ x + 22.
To test my answer, I have included a Desmos Graph that I graphed using the information provided in the question and my answer.
