Question

What is an equation of the line that passes through the point (4,1) and is perpendicular to the line 2x-y=4?

Answer 1

since the line is perpendicular the multiplication of the slopes must be -1, start by writing the perpendicular line in the form y=mx+b

$\begin{gathered} 2x-y=4 \\ y=2x-4 \end{gathered}$

then solve to find the other slope

$\begin{gathered} (2)\cdot m=-1 \\ m=-\frac{1}{2} \end{gathered}$

after having the slope use the point to find the y-intercept

$\begin{gathered} 1=-\frac{1}{2}(4)+b \\ 1=-2+b \\ 1+2=b \\ 3=b \end{gathered}$

write all as a whole equation

$y=-\frac{1}{2}x+3$