Question

What is the equation of a line that passes through the point (9,-3) and is paralel to the line whose equation is 2x-3y=6

Answer 1

-2x + 3y = -27

or

y = 2/3 x - 9

Explanation:

First convert to slope-intercept form to find the slope of the given line.

2x - 3y = 6

-3y = -2x + 6

Divide through by -3:-

y = 2/3 x - 2

x = 9 when y = -3 so using the point slope form of an equation:-

y - (-3) = 2/3 (x - 9)

y + 3 = 2/3 x - 6

y = 2/3 x - 9

The slope is the same as the given equation so the lines are parallel.

We can now change this to standard form:-

3y = 2x - 27

-2x + 3y = -27

Answer 2

y =
`(2)/(3)` x - 9

Explanation:

the equation of a line in slope- intercept form is

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

rearrange 2x - 3y = 6 into this form

subtract 2x from both sides

- 3y = - 2x + 6 ( divide all terms by - 3 )

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

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

• Parallel lines have equal slopes, hence

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

to find c substitute (9, - 3) into the partial equation

- 3 = 6 + c ⇒ c = - 3 - 6 = - 9

y =
`(2)/(3)` x - 9 ← equation of parallel line