Answer: y = - 4 x + 17
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 = ¹/₄
then the slope of the perpendicular line (m) = - 4
Determine the equation
We can now use the point-slope form (y - y₁) = m(x - x₁)) to write the equation for this line:
⇒ y - 1 = - 4 (x - 4)
∴ y - 1 = - 4 (x - 4)
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 - 1 = - 4 (x - 4)
y = - 4 x + 17
∴ the slope-intercept equation of the perpendicular line is y = - 4 x + 17.
