Question

1. Find the equation of the line that satisfies the given conditions:

(a) Perpendicular to a line with slope − 1
2 ; passing through (−1, 2)
(b) Passes through (1, 1) and is parallel to the line x + y = 1

Answer 1

y = x + 3 , y = - x + 2

Explanation:

the equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

(a)

given slope m = - 1

the product of the slopes of perpendicular lines = - 1 , then

m ×
`m_(perpendicular)` = - 1

- 1 ×
`m_(perpendicular)` = - 1 ( divide both sides by - 1 )

`m_(perpendicular)` = 1

y = x + c ← is the partial equation

to find c substitute (- 1, 2 ) into the partial equation

2 = - 1 + c ( add 1 to both sides )

3 = c

y = x + 3 ← equation of perpendicular line

(b)

given

x + y = 1 ( subtract x from both sides )

y = - x + 1 ← in slope- intercept form

with slope m = - 1

• Parallel lines have equal slopes , so

y = - x + c ← is the partial equation

to find c substitute (1, 1 ) into the partial equation

1 = - 1 + c ( add 1 to both sides )

2 = c

y = - x + 2 ← equation of parallel line