Question

What is the equation of a line that passes through the point (9, −3) and is parallel to the line whose equation is 2x−3y=6 ?

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Answer 1

parallel lines have same slope so
m=3/2
passes thorough the point 9 ,-3
so y-y1= m (x-x1)
then eq 3x-2y=-27

Answer 2

Answer: $2x-3y-27=0.$

Step-by-step explanation: The given line is $2x-3y=6$ and the point is $(9,-3)$.

Now,

$2x-3y=6\\\Rightarrow 3y=2x-6\\\Rightarrow y=\dfrac{2}{3}-2.$

So, slope of the line, $m=\dfrac{2}{3}.$

Since both the lines are parallel, so they must have equal slopes. Also, the line passes through the point $(9,-3)$, the equation of the line is given by

$y-(-3)=\dfrac{2}{3}(x-9)\\\Rightarrow 3(y+3)=2(x-9)\\\Rightarrow 3y+9=2x-18\\\Rightarrow 2x-3y-27=0.$

Thus, the required equation of the line is

$2x-3y-27$.