Proving Relationships of Parallel and Perpendicular Lines

Consider the given equation. $$\begin{array}{c}y=4x-5\end{array}$$ Recall that parallel lines have the same slope. Because of this, we know that all lines that are parallel to the given one will have a slope of $4.$ We can write a general equation in slope-intercept form for all the lines that are parallel to the given line. $$\begin{array}{c}y=4x+b\end{array}$$ Now we have to find the value of the $y\text{-}$intercept. To do so, we will substitute the given point $(\text{-}1,5)$ in the above equation, and solve for $b.$ Now that we know the value of the $y\text{-}$intercept, we write the equation of the parallel line to $y=4x-5$ through $(\text{-}1,5).$ $$\begin{array}{r}y=4x+9\end{array}$$