Question

Find the equation to the straight line parallel to $3x-4y+6=0$ and passing through the middle point of the join of points $(2,3)$ and $(4,-1).$

Answer 1

The slope of the given line is equal to the slope of line $3x-4y+6=0$ as the two lines are parallel to each other

$\therefore m_1=m_2=\frac{3}{4}$

And the line passes through mid point of points $(2,3)$ and $(4,-1)$

ie., $(\frac{2+4}{2},\frac{3-1}{2})$ [Using mid point formula]

$\Rightarrow (3,1)$

$\therefore$ Using one point-slope equation of line

$(y-1)=\frac{3}{4}(x-3)$

$4y-4=3x-9$

$3x-4y=5$

Is the required line.