Given the equation 2x - 3y = 30.

We need to find the parallel slope to the given line.

First we need to rewrite the equation of the line into the slope format.

y= mx + b

==> 2x - 3y = 30

==> -3y = -2x + 30

Now we will divide by -3:

==> y= ( -2x + 30) /- 3

==> y= ( 2/3)x + 30/-3

==> y= (2/3)x -10

Since the line is parallel to the line y = (2/3)x - 10

Then they have the same slopes:

**Then, the line that parallel to the equation of the line y is has the slope of 2/3**

Slope of any line parallel to a line is same as the slope of the original line.

We calculate slope of the given line using the following formula for slope of a line defined by ax + by = c

Slope = -a/b

The equation of the line is:

2x - 3y = 30

Substituting the values of a and b in the given equation of line:

Slope of given line = -2/(-3) = 2/3

Therefore:

Parallel slope to the given line = Slope of given line = 2/3

Answer:

Slope = 2/3

(Please not that the value of the constant (c) has no impact on the slope. We cam construct equations of parallel lines by keeping values of a and b same and chancing the value of c.)

To determine the slope parallel line to 2x-3y= 30.

We know that any line ax+by+c = 0 could be written as :

by = -bx-c. Or y = (-b/a)x+(-c/a) , where (-b/a) is its slope.

The equation of parallel line to ax+by+c is of the form ax+by+d = 0.Thus there is no change in the slope of a parallel. Or the slope of the line and parallel line es are same.

Therefore the thgive line 2x-3y = 30 in the slope interept form is:

y = (-2x+30)/3. Or y = (-2/3)x+10, whose slope is -2/3.

Therefore the slope of a parallel line to 3x-2y = 30 is also -2/3.