Question

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

Answer 1

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

Explanation: Let's rewrite the equation into standard form.


`2x - 3y = 6`

`-3y = 6 - 2x`

`3y = 2x - 6`

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

Now that it's the form y = mx + b, we know that the gradient is
`(2)/(3)`

For a line to be parallel to another line, they must contain the same gradient. Now, the point (9, -3) passes through the line, meaning the points at x = 9 and y = -3 must satisfy our equation. Since we have a point and a gradient, we can use the point-gradient form.


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

`3y + 9 = 2x - 18`

`3y = 2x - 27`


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