Question

Find an equation of the line satisfying the given conditions. Give the answer in slope-Intercept form if possible, a) Passing through (3,-4) and parallel to y = 3 + 2x b) Perpendicular to 6x +2y + 43 = 0 and passing through (1.5)

Answer 1

(a) y = 2x - 10 , (b) y =
`(1)/(3)` x +
`(14)/(3)`

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 y = 3 + 2x = 2x + 3 ← in slope- intercept form

with slope m = 2

• Parallel lines have equal slopes , then

y = 2x + c ← is the partial equation

to find c substitute (3, - 4 ) into the partial equation

- 4 = 2(3) + c = 6 + c ( subtract 6 from both sides )

- 10 = c

y = 2x - 10 ← equation of parallel line

(b)

given

6x + 2y + 43 = 0 ( subtract 6x + 43 from both sides )

2y = - 6x - 43 ( divide through by 2 )

y = - 3x - 21.5 ← in slope- intercept form

with slope m = - 3

given a line with slope m then the slope of a line perpendicular to it is

`m_(perpendicular)` = -
`(1)/(m)` = -
`(1)/(-3)` =
`(1)/(3)` , then

y =
`(1)/(3)` x + c ← is the partial equation

to find c substitute (1, 5 ) into the partial equation

5 =
`(1)/(3)` (1) + c =
`(1)/(3)` + c ( subtract
`(1)/(3)` from both sides )

`(15)/(3)` -
`(1)/(3)` = c , so c =
`(14)/(3)`

y =
`(1)/(3)` x +
`(14)/(3)` ← equation of perpendicular line