What is an equation of the line that passes through the point (-6,-2)(−6,−2) and is parallel to the line 3x-2y=23x−2y=2

y = 3/2x + 7

Step-by-step explanation:

If two lines are parallel to each other, they have the same slope.

The first line is 3x - 2y = 2. First, let's put this into standard form.

3x - 2y = 2

Add 2y to both sides to make y positive.

3x = 2y + 2

Subtract 2 from both sides to isolate y.

3x - 2 = 2y

Isolate y further by dividing both sides by 2.

3/2x - 1 = y or y = 3/2x - 1

This is now your first line. Its slope is 3/2. A line parallel to this one will also have a slope of 3/2.

Plug this value (3/2) into your standard point-slope equation of y = mx + b.

y = 3/2x + b

To find b, we want to plug in a value that we know is on this line: in this case, it is (-6, -2). Plug in the x and y values into the x and y of the standard equation.

-2 = 3/2(-6) + b

To find b, multiply the slope and the input of x (-6)

-2 = -9 + b

Now, add 9 to both sides to isolate b.

7 = b

Plug this into your standard equation.

y = 3/2x + 7

This equation is parallel to your given equation (y = 3/2x - 1) and contains point (-6, -2)

Hope this helps!