Answer :
Method 1: Realize that the desired equation will look exactly the same as the given equation 3x − 4y = 6, except that the constant will be different.
Thus, the equation of the new line is 3(-2) − 4(6) = C, where C comes out to 30.
Then the new line is 3x - 4y = 30.
Thus, the equation of the new line is 3(-2) − 4(6) = C, where C comes out to 30.
Then the new line is 3x - 4y = 30.
−3x + 4y = 30 equation of a straight line that passes through the point (−2, 6) and is parallel to the line 3x − 4y = 6.
What is a straight line?
A straight line is a line that has no curve in it even if we increase it with it's either end to the infinity.
The general equation of a straight line can be written as y = mx + c. Here, m is the gradient of the line and c is the y-intercept.
Here, the given equation is
3x − 4y = 6
⇒ -4y = - 3x + 6
⇒ y = (-3/ - 4)x + (6/ - 4)
⇒ y = (3/4)x - (3/2)
Therefore, the gradient (m) of the required straight line is 3/4.
The required straight line pass through the point (-2, 6).
Therefore, we can put this value in the general equation of straight line.
y = mx + c
⇒ 6 = (3/4) × (-2) + c
⇒ c = 6 + 3/2 = 15/2
Hence, the equation of the required straight line is:
y = (3/4)x + 15/2
⇒ 4y = 3x + 30 (multiplying either side by 4)
⇒ 4y -3x = 30
Therefore, option 3 is the right answer.
Learn more about the equation of straight line here: https://brainly.com/question/27730503
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