Question

Write an equation of the line passing through the point (3, 4) that is parallel to the line −2x+3y=2

Answer 1

Parallel lines have same slope, so first isolate y to get the equation into y=mx+b form.

-2x+3y=2

3y = 2x + 2

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

Now plug the point (3,4) into y = 2x + b

4 = 2(3) + b

Solves for be

b = -2

So the new equation is y = 2x - 2

Answer 2

Answer:

-2x + 3y = 6

Step-by-step explanation:

A line parallel to the given -2x + 3y = 2 will have the same slope, and will also have the same form, different only in the constant term:   -2x + 3y = C.

We know that this new line passes thru (3,4).  Use this info to determine C for this line.  -2(3) + 3(4) = C, or -6 + 12 = C, or C = 6.

Thus, the equation of the line thru (3,4) parallel to the given line is  -2x + 3y = 6.