Question

Write an equation for the line that passes through the point (1,5) and is perpendicular to the graph of x + 2y = 4

Answer 1

Convert the equation to slope intercept form to get

$\begin{gathered} x+2y=4 \\ x+2y-x=-x+4 \\ 2y=-x+4 \\ \frac{2y}{2}=-\frac{x}{2}+\frac{4}{2} \\ y=-\frac{1}{2}x+2 \end{gathered}$

then The old slope is -1/2 and the new slope is 2.

With the new slope, use the slope intercept form and the point to calculate the intercept: y = mx + b

$\begin{gathered} 5=2(1)+b \\ 5=2+b \\ 5-2=2+b-2 \\ b=3 \end{gathered}$

therefore, the equation is

$y=2x+3$