Question

Write the equation of the line that is parallel to line m and passes through the point (4, - 5).

Answer 1

The slope of the line parallel to the given line will be same as that of the given line.

Let 'm' be the slope of the line,

$y-b=m(x-a)$

Substitute a=4 and b=-5 in the above expression.

$\begin{gathered} y-(-5)=m\times(x-4) \\ y+5=mx-4m \\ y=mx-4m-5 \end{gathered}$

Thus, the expression of the parallel line is y=mx-4m-5.