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