a line parallel to 3x +2y - 4=0 and passing through (2;3)

Thank you very much

PS Still confused. Two lines are perpendicular if the product of their slope -1. Please detail.

Two lines are

**perpendicular **if the

**product of their slopes is -1**
and

Two lines are

**parallel** if

**their slopes are equal**
These should be stated in your book or should be taught by your instructor.

and the equation of a line passing through a point\(\displaystyle (x_1, y_1)\) is given by:

\(\displaystyle y-y_1= m(x-x_1)\) .............................(I)

Now use this above formula to find the equation of the line passing through (2,3).

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for the line \(\displaystyle 3x +2y - 4=0\)., find the slope of this line by re-writing the equation in the form of \(\displaystyle y = mx+b\); where m is the slope.

so you have : \(\displaystyle 3x +2y - 4=0 \implies 2y = -3x+4 \implies y = \frac{-3}{2}x + \frac{4}{3}\)

so the slope of this line is \(\displaystyle \frac{-3}{2}\). since the two lines are parallel, the slope of the other line should also be \(\displaystyle \frac{-3}{2}\)

so you have the point(2,3) and the slope m = -3/2. plug these in equation (I) to find the equation of the line.

This question is similar to the one you had posted before