Determine the equation of the line

Question

that is parallel to 3y-2X=6 and passes through the point (9;-1)

Answer 1

Slope - intercept form line equation is y = mx + b, where m is slope and b is y-intercept.

The line equation is 3y - 2x = 6.

Write the equation in slope - intercept form.

3y = 2x + 6

y = (2/3)x + (6/3)

y = (2/3)x + 2.

Comapare the equation with slope - intercept form.

Slope (m) = 2/3

Because the parallel lines have same slopes, the slope of parallel line through the point (9, - 1) is 2/3.

Now the parallel line equation is y = (2/3)x + b.

Find the y - intercept by substituting the point in the parallel line equation say (x, y) = (9, - 1).

- 1  = (2/3)(9) + b

b = - 1 - 6

⇒ b = - 7.

The parallel line equation is y = (2/3)x - 7.