# write an equation

#### ecdino2

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.

#### dwsmith

MHF Hall of Honor
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.
re-write
$$\displaystyle 3x+2y=4$$

any line parallel will be of the form:
$$\displaystyle 3x+2y=z,\ \forall z\in\mathbb{R}$$

#### harish21

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

#### lorica2000

of a line parallel to 3x +3y-4=0 passing through the point(2,3)

#### harish21

of a line parallel to 3x +3y-4=0 passing through the point(2,3)
refer to the steps given in Post#3 in this thread!

Show your work if you are stuck.