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 \\ (2y)/(2)=-(x)/(2)+(4)/(2) \\ y=-(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`