Question

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

Answer 1

Answer:

all work is shown and pictured

Answer 2

Answer:

2x = 30 - 3y

Step-by-step explanation:

Given equation of the line,

$2x = 1 - 3y$

$3y = - 2x + 1$

$y=-\frac{2}{3}x+\frac{1}{3}$

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

By comparing,

Slope of the line,

$m=-\frac{2}{3}$

Parallel lines have same slope,

Thus, the slope of the line parallel to the given line is also $-\frac{2}{3}$,

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,

$y-4=-\frac{2}{3}(x-9)$

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

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

$\implies 2x = 30 - 3y$