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