Write the equation of the line that satisfies the given conditions. Express the final equation in standard form. (Objectives 2 and 4) Contains the point (-4, 6

Question

Write the equation of the line that satisfies the given conditions. Express the final equation in standard form. (Objectives 2 and 4)
Contains the point
(−4, 6)
and is perpendicular to the line
x − 2y = 2

Answer 1

Contains (-4,6)

Perpendicular to x-2y=2

 

The slope of x-2y=2 is 1/2

You can find this by solving for y = (1/2)x-1

Or you can look at  the slope of  ax + by = c is m=-a/b

 

A perpendicular line will have a slope that is the

negative reciprocal of 1/2 so m = -1/(1/2) = -2

 

Your perpendicular line has point (-4,6), slope m=-2

 

Using point slope form: y-y₁ = m(x-x₁) where (x₁,y₁)=(-4,6) & m=-2

 

y-6 = -2(x-(-4))

y-6 = -2(x+4)

y-6 = -2x-8      add 2x to both sides

2x+y-6 = -8     add 6 to both sides

2x+y=-2

 

2x + y = -2    is your standard format of ax+by=c