Question

What is the equation of the line that passes through (4, 2) ) and is parallel to 3x - 2y = - 6 ?

Answer 1

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

Explanation:

The graph I provided shows it passes thru (4,2) and that it is parallel

Answer 2

y = 3/2x -4

Explanation:

3x - 2y = - 6

First find the slope by putting it in slope intercept form

Subtract 3x from each side

-2y = -3x-6

Divide by -2

y = -3x/-2 -6/-2

y = 3/2x +3

The slope is 3/2

Parallel lines have the same slope

We have the slope 3/2 and a point (4,2)

y = mx+b where m is the slope and b is the y intercept

y =3/2x+b

Substitute the point into the equation

2 = 3/2(4) +b

2 = 6 +b

Subtract 6

2-6 = 6-6+b

-4 =b

y = 3/2x -4