Question

How do you write an equation of a line going through `(1/8, −1)` and parallel to the line `8x − 9y = 6`?

Answer 1

`y= 8/9x -1 1/9`

Explanation:

Parallel lines have the same slope. So we can find the required slope from the equation of the given line.
Change it into the form `y = color(blue)(m)x+c`

`9y =8x-6`

`y = color(blue)(8/9)x-2/3" "rarr` this gives us `color(blue)(m = 8/9)`

You can use the formula: `y-y_1 = m(x-x_1)` because we have a point `(1/8, -1)` and the slope `color(blue)(m = 8/9)`

`y-y_1 = color(blue)(m)(x-x_1)`

`y -(-1) = color(blue)(8/9)(x-1/8)`

`y+1 = 8/9x -1/9" "larr [cancel8/9 xx1/cancel8 =1/9]`

`y= 8/9x -1 1/9" "larr [-1 -1/9 = -1 1/9]`

As we expected, the slope of the new line is `8/9`