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

Question

I need help if you have the answer pls be specific.

Answer 1

Parallel lines have the same slope so find the slope of the equation -2x + 3y = 2 by putting into y = mx + b form. First add 2x to both sides to get 3y = 2x + 2. Now divide all the terms by 3 to get y = 2/3x + 2/3.

Then the slope, m, = 2/3.

Now use this with the given point to put into point slope form, (y-y₁) = m(x-x₁) to get

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

Most teachers want this in y = mx + b form. Multiply both sides by 3 to clear the fraction. This gives

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

Now distribute to get 3y - 12 = 2x - 6

Add 12 to both sides to get 3y = 2x + 6

Now divide both sides by 3 to get y = 2/3x + 2