Answer:
The equation of the perpendicular line is y = -x - 2
Explanation:
* Lets revise the form of the slope intercept for
- The slope intercept form is y = mx + b, where m is the slope of
the line and b is the y-intercept
* Now lets revise the relation between the slopes of the
perpendicular lines
- If two lines are perpendicular, then the product of their slopes is -1
# Ex: If line L has slope m1 and line K has slope m2, and L ⊥ K
∴ m1 × m2 = -1
∴ m2 = -1/m1
* Now lets solve the problem
- We need to find the equation of the line which is perpendicular to
the line whose equation is y = x + 3 and passes through point (2 , -4)
- Find the slope of the given equation
∵ y = x + 3
- In this form the slope is the coefficient of x
∴ m = 1
- Find the slope of the perpendicular line
∵ The slope of the perpendicular line = -1/m
∴ The slope of it = -1/1 = -1
- Write the equation of the line with the value of the slope
∴ y = -x + b
- To find the value of b substitute x , y in the equation by the x and
y of the given point
∵ The line passes through point (2 , -4)
∵ y = -x + b
∴ -4 = -1(2) + b
∴ -4 = -2 + b ⇒ add 2 for both sides
∴ b = -2
- Write the equation with the value of b
∴ y = -x - 2