Writing equations of parallel and perpendicular lines

Question

Find r so that the line through (2,6) and (-4,r) is

a. parallel to 2x-3x=4

b. perpendicular to x+2y=1

Answer 1

Formula for slope is

 

m = (y₂ - y₁) / (x₂ - x₁)

 

Point 1 = (2, 6)

Point 2 = (-4, r)

 

 

b)

 

Perpendicular lines have negative reciprocal slope.

 

From the given equation,

 

2y = -x + 1

 

  y = (-1 / 2)x + 1/2

 

 

The line that is parallel to this one will have a slope of 2.

 

Apply the formula for slope.

 

2 = (r - 6) / (-4 - 2)

 

 

Solve for r from the slope equation.

 

 

 

a)

 

Do the same for part (a), only that parallel lines have the same slope.