Question

I need help with this math question it would be greatly appreciated.

Answer 1

equation of L₁ is y = 2x - 7

Explanation:

the equation of a line in slope- intercept form is

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

given L₂

x + 2y = 3 ( subtract x from both sides )

2y = - x + 3 ( divide through by 2 )

y = -
`(1)/(2)` x +
`(3)/(2)` ← in slope- intercept form

with slope m = -
`(1)/(2)`

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

`m_(perpendicular)` = -
`(1)/(m)` = -
`(1)/(-(1)/(2) )` = 2

slope of L₁ = 2 and passes through (3, - 1 ) , then

y = 2x + c ← is the partial equation of L₁

to find c substitute (3, - 1 ) into the partial equation

- 1 = 6 + c ⇒ c = - 1 - 6 = - 7

y = 2x - 7 ← equation of L₁