Question

Write the equation of the line that it is parallel to 2x = 1 - 3y and passes through
(9,4).

Answer 1

all work is shown and pictured

Answer 2

2x = 30 - 3y

Explanation:

Given equation of the line,

`2x = 1 - 3y`

`3y = - 2x + 1`

`y=-(2)/(3)x+(1)/(3)`

Since, the slope of a line y = mx + c is m,

By comparing,

Slope of the line,

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

Parallel lines have same slope,

Thus, the slope of the line parallel to the given line is also
`-(2)/(3)`,

Now, the equation of the line with slope m passes through
`(x_1, y_1)` is,

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

∵ Parallel line passes through ( 9, 4),

Hence, the equation of the parallel line would be,

`y-4=-(2)/(3)(x-9)`

`3y - 12 = -2x + 18`

`\implies 2x = 18 - 3y + 12`

`\implies 2x = 30 - 3y`