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

The point-slope form of the line is given by
y - k = m(x - h)
Where m is the slope and (h,k) is a point on the line.

So we are given a point on the line, (1, -2), so all we need to do is get the slope.

It is said that the slope is the same as the slope of the line
y - 4 = (2/3)(x - 3)
Which incidentally, already happens to be in the point-slope form :D
That means 2/3 is the slope.

So we have our slope (2/3) and we have our point (1, -2)
Plugging them into the point slope form, we get
y + 2 = (2/3)(x - 1)
The standard form is
Ax + By = C

y + 2 = (2/3)x - (2/3)
(2/3)x + y = -2 - (2/3)
(2/3)x + y = -(8/3)

Cheers :D