Question

Help me I keep getting it wrong

Answer 1

see explanation

Explanation:

The equation of a line in slope- intercept form is

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

y =
`(2)/(3)` x - 6 ← is in slope- intercept form

with slope m =
`(2)/(3)`

Parallel lines have equal slopes , then

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

To find c substitute (9, 2) into the partial equation

2 = 6 + c ⇒ c = 2 - 6 = - 4

y =
`(2)/(3)` x - 4 ← equation of parallel line

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

`m_(perpendicular)` = -
`(1)/(m)` = -
`(1)/((2)/(3) )` = -
`(3)/(2)` , then

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

To find c substitute (9, 2) into the partial equation

2 = -
`(27)/(2)` + c ⇒ c = 2 +
`(27)/(2)` =
`(31)/(2)`

y = -
`(3)/(2)` x +
`(31)/(2)` ← equation of perpendicular line