Answer:
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!
