Question

Indicate the equation of the given line in standard form.

The line that contains the point Q( 1, -2) and is parallel to the line whose equation is

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

Answer 1

y - 4 = 2/3(x - 3)
y - 4 = 2/3x - 2
y = 2/3x - 2 + 4
y = 2/3x + 2
As you can see, the slope of this line is 2/3. And since you want to find a parallel line, then the slope will be the same....2/3.
y = mx + b.....using slope 2/3 and points (1,-2)
-2 = 2/3(1) + b
-2 = 2/3 + b
-2 - 2/3 = b
-6/3 - 2/3 = b
- 8/3 = b

y = 2/3x - 8/3
Lets remove the fractions by multiplying by 3
3y = 2x - 8
Now we will put this in standard form
-2x + 3y = -8 (multiply by -1 to make x positive
2x - 3y = 8 <-- this is your parallel equation

Answer 2

Thanks